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

1,1

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A270353 A270400 A269999 * A230309 A102275 A299448

Adjacent sequences: A298941 A298942 A298943 * A298945 A298946 A298947

Keyword

nonn

Author

Felix Fröhlich, Jan 30 2018

Status

approved