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

0,2

Comments

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

Links

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

Formula

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

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 *)

Prog

(Haskell)
a188917 n = a188917_list !! n
a188917_list = filter ((== 1) . a209229. a188915) [0..]
-- Reinhard Zumkeller, May 19 2015
(Python)
from math import isqrt
def A188917(n): return (n+1>>1)+isqrt(1<<n) # Chai Wah Wu, Oct 01 2024

Crossrefs

Cf. A000079, A000290, A017910, A036987.

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

Sequence in context: A023434 A353035 A087192 * A046935 A241334 A374760

Adjacent sequences: A188914 A188915 A188916 * A188918 A188919 A188920

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 14 2011

Status

approved