

A115379


Number of positive integers k < n such that n XOR k < n and gcd(n,k) is odd.


1



0, 1, 0, 3, 0, 3, 2, 7, 0, 3, 2, 7, 4, 11, 6, 15, 0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 16, 35, 18, 39, 20, 43, 22, 47, 24, 51, 26, 55, 28, 59, 30, 63, 0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 16, 35
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OFFSET

0,4


COMMENTS

A059029 equals the limiting sequence of 2^k consecutive terms of this sequence starting at position 2^k as k increases, where A059029(n) = n if n is even, 2n+1 if n is odd.


LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..1000
Index entries for sequences related to the Josephus Problem


FORMULA

a(2^n) = 0, a(2^n1) = 2^n1, for n >= 0. a(2^n+1)=3 (n>0), a(2^n+2)=2 (n>1)), a(2^n+3)=7 (n>1), a(2^n+4)=4 (n>2), a(2^n+5)=11 (n>2), etc.


MATHEMATICA

Table[Sum[If[BitXor[n, k]< n && OddQ[GCD[n, k]], 1, 0], {k, 0, n}], {n, 0, 81}] (* Indranil Ghosh, Mar 16 2017 *)


PROG

(PARI) a(n)=sum(k=0, n, if(bitxor(n, k)<n&gcd(n, k)%2==1, 1, 0))


CROSSREFS

Cf. A059029, A006257 (Josephus problem).
Sequence in context: A112470 A331924 A201582 * A127801 A096597 A097994
Adjacent sequences: A115376 A115377 A115378 * A115380 A115381 A115382


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Jan 21 2006


STATUS

approved



