A337921 a(n) is the sum of (3^n mod 2^k) for k such that 2^k < 3^n.

1, 3, 18, 38, 195, 585, 607, 3948, 11976, 42415, 127921, 56067, 666938, 2082798, 10769251, 22610393, 110616780, 315726436, 408228944, 2384863439, 7159829169, 23350950650, 74348867826, 49863537606, 401947783347, 1296027221145, 6159163094580, 13796041908620, 60717334308629, 181812784262527

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 29 2021

Keywords

• nonn

Comments

a(n) == A056576(n) (mod 2).

Examples

			a(3) = (3^3 mod 2^1) + (3^3 mod 2^2) + (3^3 mod 2^3) + (3^3 mod 2^4) = 18.
		

Links

• Robert P. P. McKone, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A056576.

Programs

Maple

f:= proc(n) local k; add(3 &^ n mod 2^k, k = 1 .. ilog2(3^n)) end proc:
map(f, [$1..100]);

Mathematica

A337921[n_] := Sum[Mod[3^n, 2^k], {k, 1, Floor[n*Log[2, 3]]}]; Table[A337921[n], {n, 1, 30}] (* Robert P. P. McKone, Jan 31 2021 *)

PARI

a(n) = sum(k=1, logint(3^n, 2), lift(Mod(3, 2^k)^n)); \\ Michel Marcus, Jan 30 2021