A188917 Where powers of 2 occur in the union of squares and powers of 2.

1, 2, 3, 4, 6, 8, 11, 15, 20, 27, 37, 51, 70, 97, 135, 189, 264, 371, 521, 734, 1034, 1459, 2059, 2908, 4108, 5805, 8205, 11599, 16398, 23185, 32783, 46356, 65552, 92698, 131089, 185381, 262162, 370746, 524307, 741475, 1048596, 1482931, 2097173, 2965842, 4194326, 5931664, 8388631

Offset: 0

Author

Reinhard Zumkeller, Apr 14 2011

Keywords

• nonn
• easy

Comments

A188915(a(n)) = A000079(n); A188915(A188916(n)) = A000290(n).

Links

• Robert Israel, Table of n, a(n) for n = 0..6637

Crossrefs

Cf. A000079, A000290, A017910, A036987.

Cf. A188915, A188916, A209229, A006127 (subsequence).

Programs

Haskell

a188917 n = a188917_list !! n
a188917_list = filter ((== 1) . a209229. a188915) [0..]
-- Reinhard Zumkeller, May 19 2015

Maple

seq(floor((n+1)/2) + floor(2^(n/2)), n=0..100); # Robert Israel, Jun 13 2019

Mathematica

Table[Floor[(n+1)/2] + Floor[2^(n/2)], {n, 0, 50}] (* Paolo Xausa, Oct 01 2024 *)

Python

from math import isqrt
def A188917(n): return (n+1>>1)+isqrt(1<Chai Wah Wu, Oct 01 2024

Formula

a(n) = floor((n+1)/2) + floor(2^(n/2)). - Robert Israel, Jun 13 2019