A256517 Let c be the n-th composite number. Then a(n) is the smallest base b > 1 such that b^(c-1) == 1 (mod c^2), i.e., such that c is a 'Wieferich pseudoprime'.

17, 37, 65, 80, 101, 145, 197, 26, 257, 325, 401, 197, 485, 577, 182, 677, 728, 177, 901, 1025, 485, 1157, 99, 1297, 1445, 170, 1601, 1765, 1937, 82, 2117, 2305, 1047, 2501, 577, 529, 2917, 1451, 3137, 721, 3365, 3601, 3845, 244, 4097, 99, 1945, 4625, 530

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..3000 from Felix Fröhlich)

Formula

a(n) = A185103(A002808(n)-1). - Bill McEachen, Nov 27 2021

Mathematica

c = Select[Range@ 69, CompositeQ]; f[c_] := Block[{b = 2}, While[Mod[b^(c - 1), c^2] != 1, b++]; b]; f /@ c (* Michael De Vlieger, Apr 03 2015 *)

Prog

(PARI) forcomposite(c=1, 1e3, b=2; while(Mod(b, c^2)^(c-1)!=1, b++); print1(b, ", "))
(Python)
from sympy import composite
from sympy.ntheory.residue_ntheory import nthroot_mod
def A256517(n):
    z = nthroot_mod(1, (c := composite(n))-1, c**2, True)
    return int(z[0]+c**2 if len(z) == 1 else z[1]) # Chai Wah Wu, May 18 2022

Crossrefs

Cf. A039678, A242742, A244752, A255885.

Cf. A185103, A002808.

Sequence in context: A269788 A146348 A050952 * A323603 A200865 A319245

Adjacent sequences: A256514 A256515 A256516 * A256518 A256519 A256520

Keyword

nonn

Author

Felix Fröhlich, Apr 01 2015

Status

approved