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A298944
a(n) = 2^(c-1) mod c^2, where c is the n-th composite number.
3
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
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)), ", "))
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jan 30 2018
STATUS
approved