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A090897
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Next n digits of Pi.
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8
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3, 14, 159, 2653, 58979, 323846, 2643383, 27950288, 419716939, 9375105820, 97494459230, 781640628620, 8998628034825, 34211706798214, 808651328230664, 7093844609550582, 23172535940812848, 111745028410270193, 8521105559644622948, 95493038196442881097
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OFFSET
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1,1
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COMMENTS
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More precisely: the integer resulting from reading the "next n digits of Pi" in base 10, so leading zeros cannot be directly seen, but easily be "reconstructed" from the fact that the term will have less than n digits although it is made from n digits of Pi. - M. F. Hasler, Jan 06 2023
It seems that all terms have at least one prime factor that does not appear in the combined list of prime factors of the preceding terms of the sequence. - Mario Cortés, Aug 20 2020 [Checked up to n=65. - Michel Marcus, Aug 21 2020]
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LINKS
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FORMULA
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a(n) = floor( Pi * 10^(n*(n+1)/2-1) ) mod (10^n). - Carl R. White, Aug 13 2010
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EXAMPLE
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a(3) = 159 because after the first (a(1) = 3) and the next two digits of Pi (a(2) = 14) the next three are 159.
Other examples are as follows and fall into a triangular digit pattern, though there is no guarantee that they will remain triangular in all cases
a(1) = 3;
a(2) = 14;
a(3) = 159;
a(4) = 2653;
a(5) = 58979;
(End)
Indeed, precisely whenever A086639(n) = 0, then the corresponding term of this sequence will lack one or more leading zeros and therefore the above list will deviate from the triangular shape. - M. F. Hasler, Jan 06 2023
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MAPLE
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Partitioner := proc(cons, len) local i, R, spl; R := []; i:=0;
spl := L -> [seq([seq(L[i], i=1 + n*(n+1)/2..(n+1)*(n+2)/2)], n=0..len)]:
ListTools:-Reverse(convert(floor(cons*10^((len+1)*(len+2)/2)), base, 10)):
map(`@`(parse, cat, op), spl(%)) end:
aList := -> Partitioner(Pi, 20); aList(20); # Peter Luschny, Aug 22 2020
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MATHEMATICA
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With[{pi=RealDigits[Pi, 10, 500][[1]]}, FromDigits/@Table[Take[pi, {n (n-1)/2+1, (n(n+1))/2}], {n, 25}]] (* Harvey P. Dale, Dec 24 2011 *)
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PROG
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(PARI) lista(nn) = {my(nd = 5+nn*(nn+1)/2); default(realprecision, nd); my(vd = digits(floor(Pi*10^nd))); my(pos = 1); my(vr = vector(nn)); for (n=1, nn, vr[n] = fromdigits(vector(n, k, vd[k+ pos-1])); pos += n; ); vr; } \\ Michel Marcus, Aug 21 2020
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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