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A258367 Smallest A (in absolute value) such that for p=prime(n), 2^{(p-1)/2} == +-1 + A*p (mod p^2), i.e., such that p is a near-Wieferich prime. 6
1, 1, 1, 3, 5, 2, 8, 3, 14, 3, 18, 9, 9, 22, 18, 4, 18, 5, 1, 28, 30, 24, 3, 20, 46, 22, 47, 21, 15, 9, 57, 42, 15, 48, 28, 41, 48, 60, 85, 25, 74, 25, 52, 11, 32, 51, 17, 13, 34, 113, 13, 71, 2, 16, 64, 130, 81, 35, 37, 29, 39, 147, 68, 60, 71, 96, 92, 99, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

p is in A001220 iff a(n) == 0. This is the case iff A014664(n) == A243905(n), which happens for n = 183 and n = 490.

Is a(n) == 0 for any other n, and, if yes, are there infinitely many such n?

LINKS

Felix Fröhlich, Table of n, a(n) for n = 2..10000

R. Crandall, K. Dilcher and C. Pomerance, A search for Wieferich and Wilson primes, Math. Comp., 66 (1997), 433-449.

PROG

(PARI) minaval(n) = a=0; while(Mod(2, n^2)^((n-1)/2)!=1+a*n && Mod(2, n^2)^((n-1)/2)!=-1+a*n && Mod(2, n^2)^((n-1)/2)!=1-a*n && Mod(2, n^2)^((n-1)/2)!=-1-a*n, a++); a

forprime(p=3, 1e4, print1(minaval(p), ", "))

(PARI) a(n, p=prime(n))=abs(centerlift(Mod(2, p^2)^((p-1)/2))\/p)

apply(p->a(0, p), primes(100)[2..100]) \\ Charles R Greathouse IV, Jun 15 2015

CROSSREFS

Cf. A001220, A195988, A241014, A244801, A246568, A250406, A250407.

Sequence in context: A180077 A095749 A137988 * A160092 A282348 A026193

Adjacent sequences:  A258364 A258365 A258366 * A258368 A258369 A258370

KEYWORD

nonn

AUTHOR

Felix Fröhlich, May 28 2015

STATUS

approved

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Last modified October 18 04:28 EDT 2019. Contains 328145 sequences. (Running on oeis4.)