A339531 Numbers b > 1 such that the smallest two primes, i.e., 2 and 3 are base-b Wieferich primes.

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

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

From Chai Wah Wu, Aug 18 2025: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.

G.f.: x*(-x^2 + 20*x + 17)/((x - 1)^2*(x + 1)). (End)

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 * A363040 A295338 A059425

Adjacent sequences: A339528 A339529 A339530 * A339532 A339533 A339534

Keyword

nonn

Author

Felix Fröhlich, Dec 08 2020

Status

approved