A260507 -id:A260507 - cp's OEIS frontend

A260531 a(n) = (2^p+1)^(p-1) modulo p^2, where p is prime(n).

1, 0, 21, 1, 45, 79, 120, 305, 484, 697, 404, 186, 1354, 603, 612, 2757, 945, 3051, 3552, 498, 950, 1186, 2657, 1781, 6403, 9192, 8035, 1927, 2181, 2713, 6097, 2621, 10139, 3476, 10878, 8608, 22609, 21028, 24550, 19031, 1, 12852, 33426, 27793, 34279, 11543

Offset: 1

Felix Fröhlich, Jul 28 2015

nonn

The primes where a(n) == 1 are given by A260507.

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Cf. A000040, A098640, A260507.

f[n_] := Block[{p = Prime@ n}, PowerMod[2^p + 1, p - 1, p^2]]; Array[f, 46] (* Robert G. Wilson v, Jul 29 2015 *)

a(n) = lift(Mod(2^prime(n)+1, prime(n)^2)^(prime(n)-1))

a(n) = A098640(n)^(A000040(n)-1) modulo A000040(n)^2.

A259502 Primes p such that nextprime(p + 1)^(p - 1) == 1 (mod p^2).

Original entry on oeis.org

5, 47, 151051, 240727, 911135839

Offset: 1

Felix Fröhlich, Nov 08 2015

Nextprime as defined in A007918.
These are Wieferich primes p to a prime base q where the difference between p and q has minimal or almost minimal (if the difference between p and the previous prime is smaller) value.
No further terms up to 10^9.

Cf. A001220, A007918, A244546, A260377, A260507.

forprime(p=1, , if(Mod(nextprime(p+1), p^2)^(p-1)==1, print1(p, ", ")))

cp's OEIS Frontend

A260531 a(n) = (2^p+1)^(p-1) modulo p^2, where p is prime(n).

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