A178985 Primes of the form 3^k mod 2^k, in the order in which they are found.

3, 19, 11, 227, 1019, 269201, 186023729, 457933343698297657, 2267602862220213494836920572800947269169358383491, 3510117420185552058703020362961660520827436011216742688744177

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 03 2011

Keywords

• nonn

Comments

Can it be shown that this is always an increasing sequence?

{a(n)} is an increasing sequence because {a(n)} is a subsequence of the integer sequence {b(n)} = (fractional part of (3/2)^n without the decimal point)/5^n = A204544(n) / 5^n = prime terms of A002380. - Michel Lagneau, Jan 25 2012

Corresponding n: 3, 5, 7, 9, 11, 20, 28, 62, 161, 204, 471, 505, 881, 1810, 1812, 2506, 3321, ... - Eric Chen, Jun 13 2018

Links

• Eric Chen, Table of n, a(n) for n = 1..17

Crossrefs

Cf. A002380, A007520, A204544.

Programs

Mathematica

f[n_] := PowerMod[3, n, 2^n]; Select[f@ Range@ 300, PrimeQ]