OFFSET
1,1
COMMENTS
Set of terms from sequence A052983.
a(n) is the binary expansion of A043569(n). - Michel Marcus, Sep 04 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Luboš Pick, Dirichletovy šuplíčky, Pokroky matematiky, fyziky a astronomie, Vol. 61, No. 2 (2016), pp. 106-118. (In Czech; The Dirichlet pigeonhole principle)
FORMULA
A227362(a(n)) = 10.
From Robert Israel, Sep 02 2016: (Start)
a((m^2-m)/2+j) = 10^(m+1)*(1-10^(-j))/9 for m>=1, 1<=j<=m.
a(n) = 10*(10^m - 10^(-n+m*(m+1)/2))/9 where m = A002024(n). (End)
Sum_{n>=1} 1/a(n) = A073668. - Amiram Eldar, Feb 20 2022
EXAMPLE
60 is of the form binomial(a, 2) + b where 0 < b <= a and a = 11, b = 5. So a(60) has (11 + 1) digits and 5 leading ones. The other digits are 0. Giving a(60) = 111110000000. It has 7 (more than 1) trailing zeros so the next one, a(61) is a(60) + 10^(7 - 1). - David A. Corneth, Aug 30 2016
MAPLE
seq(seq(10^(m+1)*(1-10^(-j))/9, j=1..m), m=1..20); # Robert Israel, Sep 02 2016
MATHEMATICA
Table[FromDigits@ Join[ConstantArray[1, #1], ConstantArray[0, #2]] & @@@ Transpose@ {#, n - #} &@ Range[n - 1], {n, 2, 9}] // Flatten (* Michael De Vlieger, Aug 30 2016 *)
Flatten[Table[FromDigits[Join[PadRight[{}, n, 1], PadRight[{}, k, 0]]], {n, 8}, {k, 8}]]//Sort (* Harvey P. Dale, Jan 09 2019 *)
PROG
(Magma) [n: n in [1..10^7] | Seqint(Setseq(Set(Sort(Intseq(n))))) eq 10 and Seqint(Sort((Intseq(n)))) eq n]
(PARI) is(n) = vecmin(digits(n))==0 && vecmax(digits(n))==1 && digits(n)==vecsort(digits(n), , 4) \\ Felix Fröhlich, Aug 30 2016
(PARI) a(n) = my(r = ceil((sqrt(1+8*n)+1)/2), k = n - binomial(r-1, 2)); 10^(r-k)*(10^(k)-1)/9
\\ given an element n, computes the next element of the sequence.
nxt(n) = my(d = digits(n), qd=#d, s = vecsum(d)); if(qd-s>1, n+10^(qd-s-1), 10^qd)
\\ given an element n of the sequence, computes its place in the sequence.
inv(n) = my(d = digits(n)); binomial(#d-1, 2) + vecsum(d) \\ David A. Corneth, Aug 31 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Aug 30 2016
STATUS
approved