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A385856

Near-Wieferich primes (primes p satisfying 2^p == 2 + A*p (mod p^2)) with |A| <= 10.

2, 3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 47, 71, 157, 173, 211, 251, 263, 379, 383, 1093, 1097, 1699, 1753, 2633, 2659, 3373, 3511, 3593, 5501, 8089, 10691, 15823, 27967, 30577, 45827, 46477, 1437049, 1483597, 1897121, 2152849, 6266543, 52368101, 110057537, 126233057, 1683955849, 2001907169, 13211006161, 47004625957

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OFFSET

1,1

COMMENTS

Near-Wieferich primes: 2^p == 2 + A*p (mod p^2) for |A| <= 10. Extends the Wieferich condition by allowing small symmetric offsets.

See also A246568 for a related formulation involving the same congruence structure.

All values verified for p <= 5*10^10.

LINKS

Table of n, a(n) for n=1..50.

A. Lamek, User profile with notes on Wieferich-related structures

EXAMPLE

p=11: 2^11 == 2048 == 2+(-1)*11 == -9 == 112 (mod 121), so A=-1.