A283973 Numbers n such that A007306(n) = A283986(n); positions of zeros in A283988.

1, 3, 4, 9, 10, 12, 13, 15, 16, 21, 22, 27, 28, 33, 36, 37, 48, 49, 60, 61, 64, 78, 84, 85, 87, 88, 90, 91, 93, 94, 99, 100, 102, 103, 105, 106, 108, 109, 115, 129, 130, 133, 135, 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

Offset: 1

Author

Antti Karttunen, Mar 21 2017

Keywords

• nonn
• base

Comments

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A283974 (complement).

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

Programs

Mathematica

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 *)

PARI

A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
D(n) = if(n<1, 1, sum(k=0, n, binomial(n + k - 1, 2*k)%2)) /* A007306 */
for(n=1, 300, if(bitor(A(n - 1), A(n)) == D(n), print1(n,", "))) \\ Indranil Ghosh, Mar 23 2017