Search: a264848 -id:a264848
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A261696
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a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 17-gonal: (15n^2 - 13n)/2.
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+10
6
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OFFSET
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1,2
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COMMENTS
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There are some interesting patterns observed in the terms. Terms a(5), a(6), a(9), a(10), a(11), a(12), ... share the same prefix of 6798483...
From terms a(n) for n > 5, there seems to a pattern of how they are constructed from previous terms. a(6) is formed by inserting 3483...3 between the penultimate digit and the last digit of a(5). Then a(7) and (8) do not follow this pattern.
The digits of a(9) and a(6) match until the last digit of a(6). Next, a(10), a(11) and (12) are formed from a(9), a(10) and a(11) resp. by inserting 3483...3. Then this pattern is interrupted by a(13) and a(14), and continue again for a(15) ..., etc.
(End)
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LINKS
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EXAMPLE
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1, 17, 17689, 176896797 are 17-gonal.
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PROG
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(PARI) heptadecagonal(n)=ispolygonal(n, 17)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!heptadecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))
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CROSSREFS
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Cf. A051671, A051869 (17-gonal numbers), A061109, A061110, A264733, A264738, A264776, A264777, A264842, A264848, A264849, A264804.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A264733
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a(n) is the smallest number > 1 such that the concatenation a(1)a(2)...a(n) is a perfect power.
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+10
6
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4, 9, 13, 31556, 4433200001, 7330164793357114944, 364233003001227343654904892703798707409, 30558883460500823396683989630832748682356643682219859233661160618544138815441
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OFFSET
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1,1
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LINKS
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MAPLE
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a[1]:= 4: C:= 4:
for n from 2 to 9 do
looking:= true;
for d from 1 while looking do
L:= 10^d*C + 10^(d-1);
U:= 10^d*C + 10^d - 1;
p:= 1;
while p < ilog2(U) do
p:= nextprime(p);
Lp:= ceil(L^(1/p));
Up:= floor(U^(1/p));
while not (Lp::integer and Up::integer) do
Digits:= 2*Digits;
Lp:= eval(Lp);
Up:= eval(Up);
od;
if Lp <= Up then
Cp:= Lp^p;
a[n]:= Cp - 10^d*C;
C:= Cp;
looking:= false;
break
fi
od
od
od:
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MATHEMATICA
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a = {}; Do[k = 2; While[! Or[# == 1, GCD @@ FactorInteger[#][[All, -1]] > 1] &@ FromDigits@ Flatten@ Join[#, IntegerDigits@ k], k++] &@ Map[IntegerDigits, a]; AppendTo[a, k], {i, 4}]; a (* Michael De Vlieger, Jan 23 2017 *)
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PROG
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(PARI) first(m)=my(s="4"); print1(4, ", "); for(i=2, m, n=1; while(!ispower(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))
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CROSSREFS
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Cf. A001597(perfect powers), A051671, A061109, A061110, A261696, A264738, A264776, A264777, A264804, A264842, A264848, A264849.
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KEYWORD
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nonn,base,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A264804
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a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 11-gonal: (9n^2 - 7n)/2.
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+10
6
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1, 1, 526, 64095, 21420730041, 4528059468080555555556, 3834345160635370971474665069772601398563211, 100751687713984558500838936986634939491022212000570658953744730444103042117925197608458
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OFFSET
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1,3
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LINKS
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PROG
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(PARI) hendecagonal(n)=ispolygonal(n, 11)
first(m)=my(v=vector(m), s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!hendecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))
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CROSSREFS
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Cf. A051671, A051682 (11-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264842, A264848, A264849.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A264842
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a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 13-gonal: (11n^2 - 9n)/2.
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+10
6
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1, 13, 1336, 133654765 are 13-gonal.
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PROG
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(PARI) tridecagonal(n)=ispolygonal(n, 13)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!tridecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))
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CROSSREFS
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Cf. A051671, A051865 (13-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264848, A264849, A264804.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A264849
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a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 23-gonal: (21n^2 - 19n)/2.
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+10
6
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1, 30, 648, 6701456, 72020220595275, 970458695858595792221157266, 3377345920936319088412440649783459968197698452784332095, 7477788200541027929765479736500643733301085903714718188060185368351929896324223859775571543015918781111399506
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1, 130, 130648 are 23-gonal.
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PROG
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(PARI) icositrigonal(n)=ispolygonal(n, 23)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!icositrigonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))
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CROSSREFS
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Cf. A051671, A051875 (23-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264842, A264848, A264804.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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