A034939 a(n) is smallest number such that a(n)^2 + 1 is divisible by 5^n.

0, 2, 7, 57, 182, 1068, 1068, 32318, 110443, 280182, 3626068, 23157318, 120813568, 123327057, 1097376068, 11109655182, 49925501068, 355101282318, 355101282318, 3459595983307, 15613890344818, 110981321985443

Offset

0,2

Links

Zak Seidov, Table of n, a(n) for n = 0..100

Formula

a(n) = min(A048898(n), A048899(n)).

Mathematica

b=2; n5=5; jo=Join[{0, b}, Table[n5=5*n5; b=PowerMod[b, 5, n5]; b=Min[b, n5-b], {99}]] (* Zak Seidov, Nov 04 2011 *)
Table[x/.FindInstance[Mod[x^2+1, 5^n]==0, x, Integers][[1]], {n, 0, 25}] (* Harvey P. Dale, Jul 04 2017 *)

Prog

(PARI) b(n)=if(n<2, 2, b(n-1)^5)%5^n; a(n)=min(b(n), 5^n-b(n))
(Python)
from sympy.ntheory import sqrt_mod
def A034939(n): return int(sqrt_mod(-1, 5**n)) # Chai Wah Wu, May 17 2022

Crossrefs

Cf. A034935, A199206.

Cf. A048898, A048899.

Sequence in context: A304984 A002658 A175818 * A048898 A034935 A337833

Adjacent sequences: A034936 A034937 A034938 * A034940 A034941 A034942

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Michael Somos

Status

approved