A298944 a(n) = 2^(c-1) mod c^2, where c is the n-th composite number.

8, 32, 0, 13, 12, 32, 156, 184, 0, 176, 288, 319, 464, 320, 341, 496, 40, 64, 212, 0, 301, 308, 9, 1040, 952, 472, 1088, 1544, 800, 391, 508, 2048, 1191, 1312, 922, 2608, 284, 2359, 1920, 688, 1800, 3488, 2668, 2524, 0, 2291, 428, 144, 3109, 2612, 1472, 2888

Offset: 1

Author

Felix Fröhlich, Jan 30 2018

Keywords

• nonn

Comments

a(n) = 0 iff c is a term of A000079 > 4.

Composites c where a(n) = 1 could be called "Wieferich pseudoprimes". Do any such composites exist?

A necessary condition for c to be a "Wieferich pseudoprime" would be that it is a term of both A001567 and A270833 (see comments in A240719).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A001220, A001567, A240719, A270833, A298945, A298946.

Programs

Maple

map(c -> 2&^(c-1) mod c^2, remove(isprime, [$4..1000])); # Robert Israel, Feb 27 2018

Mathematica

composite[n_Integer] := FixedPoint[n + PrimePi@ # + 1 &, n + PrimePi@ n + 1]; Array[With[{c = composite@ #}, Mod[2^(c - 1), c^2]] &, 52] (* Michael De Vlieger, Jan 31 2018, composite function by Robert G. Wilson v at A066277 *)

PARI

forcomposite(c=1, 200, print1(lift(Mod(2, c^2)^(c-1)), ", "))