A266539 Terms of A006257 (Josephus problem) repeated.

0, 0, 1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 5, 5, 7, 7, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25

Offset

1,7

Comments

First differs from both A266509 and A266529 at a(25), and shares with them infinitely many terms.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Index entries for sequences related to the Josephus Problem

Formula

G.f.: (x^2 + x^4)/(1 - x - x^2 + x^3) - (1 - x)^(-1)*Sum_{k>=1} 2^k*x^(2^(k+1)). - Robert Israel, Jan 13 2016

Example

Written as an irregular triangle in which the row lengths are twice the terms of A011782 the sequence begins:
   0, 0;
   1, 1;
   1, 1, 3, 3;
   1, 1, 3, 3, 5, 5, 7, 7;
   1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15;
   ...
Row sums give 0 together with A004171.

Maple

A006257[0]:=0: for n from 1 to 100 do A006257[n]:=(A006257[n-1]+1) mod n +1: end do:
seq(A006257[i]$2, i=0..100); # Robert Israel, Jan 13 2016

Mathematica

Join[{0, 0}, Table[SeriesCoefficient[(1 + x^2)/((-1 + x)^2 (1 + x)), {x, 0, m}], {n, 6}, {m, 0, 2^n - 1}]] // Flatten (* Michael De Vlieger, Jan 05 2016 *)

Crossrefs

Partial sums give A266540.

Cf. A004171, A006257, A011782, A256249, A266509, A266529, A266535.

Sequence in context: A349813 A266529 A266509 * A090569 A160324 A347026

Adjacent sequences: A266536 A266537 A266538 * A266540 A266541 A266542

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 02 2016

Extensions

Offset changed to 1 by Ivan Neretin, Feb 09 2017

Status

approved