A283973 - OEIS

%I #18 Jun 02 2017 22:21:17

%S 1,3,4,9,10,12,13,15,16,21,22,27,28,33,36,37,48,49,60,61,64,78,84,85,

%T 87,88,90,91,93,94,99,100,102,103,105,106,108,109,115,129,130,133,135,

%U 136,141,144,145,153,159,160,162,171,172,189,190,192,193,195,196,213,214,223,225,226,232,240,241,244,249,250,252,255,256

%N Numbers n such that A007306(n) = A283986(n); positions of zeros in A283988.

%C Equally, numbers n for which A007306(n) = A283987(n), or equally, numbers n for which A283986(n) = A283987(n).

%C Numbers n such that the binary representations of A002487(n-1) and A002487(n) have no 1-bits in common shared positions.

%H Antti Karttunen, <a href="/A283973/b283973.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%t a[0] = 0; a[1] = 1; a[n_] := If[EvenQ@ n, a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Map[Function[n, If[EvenQ@ n, a[n/2], BitOr[a[#], a[# + 1]] &[(n - 1)/2]]], 2 Range[99] - 1] (* _Michael De Vlieger_, Mar 22 2017 *)

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A283973 (ZERO-POS 1 1 A283988))

%o (PARI) A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));

%o D(n) = if(n<1, 1, sum(k=0, n, binomial(n + k - 1, 2*k)%2)) /* A007306 */

%o for(n=1, 300, if(bitor(A(n - 1), A(n)) == D(n), print1(n,", "))) \\ _Indranil Ghosh_, Mar 23 2017

%Y Cf. A283974 (complement).

%Y Cf. A002487, A007306, A283986, A283987, A283988.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Mar 21 2017