A331021 Numbers k such that gcd(k^2, 2^(k-1) - 1) > k.

1093, 3511, 398945, 796797, 1592501, 1990353, 2388205, 3183909, 3581761, 4377465, 5173169, 5968873, 6165316, 10345245, 11538801, 15119469, 16313025, 17506581, 18302285, 20291545, 23076509, 23872213, 24650731, 26657177, 29442141, 36205625, 36974341, 37001329, 38194885

Offset

1,1

Comments

Conjecture: each term is a multiple of a Wieferich prime.

Prime numbers in this sequence are the Wieferich primes A001220.

Pseudoprime (A001567) terms are 3581761, 5173169, 5968873, 23872213, 36974341, 53711113, ...

The terms of A291194 that are not in this sequence are 1194649, 2786057, 3979613, 4775317, 5571021, ....

Links

Giovanni Resta, Table of n, a(n) for n = 1..4184 (terms < 10^12)

Example

1093 is a term since gcd(1093^2, 2^1092 - 1) = 1093^2 > 1093.

Mathematica

seqQ[n_] := GCD[n^2, PowerMod[2, n - 1, n^2] - 1] > n; Select[Range[10^7], seqQ]

Prog

(PARI) isok(n) = gcd(n^2, 2^(n-1) - 1) > n; \\ Michel Marcus, Jan 07 2020

Crossrefs

Cf. A001220, A001567.

Subsequence of A291194.

Sequence in context: A265630 A355545 A291194 * A270833 A273471 A266829

Adjacent sequences: A331018 A331019 A331020 * A331022 A331023 A331024

Keyword

nonn

Author

Amiram Eldar and Thomas Ordowski, Jan 07 2020

Status

approved