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A339531 Numbers b > 1 such that the smallest two primes, i.e., 2 and 3 are base-b Wieferich primes. 6
17, 37, 53, 73, 89, 109, 125, 145, 161, 181, 197, 217, 233, 253, 269, 289, 305, 325, 341, 361, 377, 397, 413, 433, 449, 469, 485, 505, 521, 541, 557, 577, 593, 613, 629, 649, 665, 685, 701, 721, 737, 757, 773, 793, 809, 829, 845, 865, 881, 901, 917, 937, 953 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..53.

FORMULA

a(n) = 4*A263941(n) + 1 for n>=2, a(n) = 4*floor((9*n)/2) + 1 for all n. - Hugo Pfoertner, Dec 08 2020

MATHEMATICA

Select[Range[2, 10^3], Function[b, AllTrue[{2, 3}, PowerMod[b, (# - 1), #^2] == 1 &]]] (* Michael De Vlieger, Dec 10 2020 *)

PROG

(PARI) is(n) = forprime(p=1, 3, if(Mod(n, p^2)^(p-1)!=1, return(0))); 1

CROSSREFS

Cf. A256236, A263941. Row 1 of A319059.

Cf. smallest k primes are base-b Wieferich primes: A339532 (k=3), A339533 (k=4), A339534 (k=5), A339535 (k=6), A339536 (k=7), A339537 (k=8).

Sequence in context: A177835 A075698 A165493 * A295338 A059425 A341937

Adjacent sequences:  A339528 A339529 A339530 * A339532 A339533 A339534

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Dec 08 2020

STATUS

approved

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Last modified February 26 14:41 EST 2021. Contains 341632 sequences. (Running on oeis4.)