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A034939 a(n) is smallest number such that a(n)^2 + 1 is divisible by 5^n. 23


%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))

%Y Cf. A034935, A199206.

%K nonn,nice,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Michael Somos_

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)