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%I #26 May 18 2022 07:59:28
%S 0,2,7,57,182,1068,1068,32318,110443,280182,3626068,23157318,
%T 120813568,123327057,1097376068,11109655182,49925501068,355101282318,
%U 355101282318,3459595983307,15613890344818,110981321985443
%N a(n) is smallest number such that a(n)^2 + 1 is divisible by 5^n.
%H Zak Seidov, <a href="/A034939/b034939.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = min(A048898(n), A048899(n)).
%t 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 *)
%t Table[x/.FindInstance[Mod[x^2+1,5^n]==0,x,Integers][[1]],{n,0,25}] (* _Harvey P. Dale_, Jul 04 2017 *)
%o (PARI) b(n)=if(n<2,2,b(n-1)^5)%5^n; a(n)=min(b(n),5^n-b(n))
%o (Python)
%o from sympy.ntheory import sqrt_mod
%o def A034939(n): return int(sqrt_mod(-1,5**n)) # _Chai Wah Wu_, May 17 2022
%Y Cf. A034935, A199206.
%Y Cf. A048898, A048899.
%K nonn,nice,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Michael Somos_
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