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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Links

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

Crossrefs

Cf. A034935, A199206.

Cf. A048898, A048899.

Programs

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 *)

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

Formula

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

Extensions

More terms from Michael Somos