A103166 a(n) = reverse(2^n) mod 2^n.

0, 0, 0, 13, 23, 46, 53, 140, 215, 105, 210, 2808, 2918, 15593, 21187, 63556, 7987, 179118, 358137, 466945, 420750, 4034914, 8068838, 10946113, 23445533, 46880176, 22406063, 117663950, 219078635, 1060248229, 2021396468, 2632727628, 2954399858, 13837158803

Offset

1,4

Comments

Remainder if (2^n written backwards) is divided by 2^n.

Links

Robert Israel, Table of n, a(n) for n = 1..3305

Formula

a(n) = A103168(2^n). - Robert Israel, Apr 30 2026

Example

a(4) = reverse(2^4) mod 2^4 = reverse(16) mod 16 = 61 mod 16 = 13.

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
seq(rev(2^n) mod 2^n, n=1..100); # Robert Israel, Apr 30 2026

Mathematica

Table[Mod[FromDigits[Reverse[IntegerDigits[2^n]]], 2^n], {n, 1, 256}]

Prog

(Python)
def a(n): t = 2**n; return int(str(t)[::-1])%t
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Dec 12 2021

Crossrefs

Cf. A002113, A071590, A103167, A103168.

Sequence in context: A320752 A213665 A068712 * A154863 A194156 A139863

Adjacent sequences: A103163 A103164 A103165 * A103167 A103168 A103169

Keyword

base,nonn

Author

Labos Elemer, Jan 28 2005

Status

approved