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%I #6 Jun 24 2015 06:42:14
%S 3,7,57,443,2057,14557,45807,110443,1672943,6139557,25670807,
%T 123327057,123327057,5006139557,19407922943,102662389557,407838170807,
%U 3459595983307,3459595983307,79753541295807,110981321985443,110981321985443,9647724486047943,9647724486047943
%N a(n) is the unique odd-valued residue modulo 5^n of a number m such that m^2+1 is divisible by 5^n.
%C For any positive integer n, if a number of the form m^2+1 is divisible by 5^n, then m mod 5^n must take one of two values--one even, the other odd. This sequence gives the odd residue. (The even residues are in A258929.)
%e If m^2+1 is divisible by 5, then m mod 5 is either 2 or 3; the odd value is 3, so a(1)=3.
%e If m^2+1 is divisible by 5^2, then m mod 5^2 is either 7 or 18; the odd value is 7, so a(2)=7.
%e If m^2+1 is divisible by 5^3, then m mod 5^3 is either 57 or 68; the odd value is 57, so a(3)=57.
%Y Cf. A048898, A048899, A257366, A258929.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Jun 23 2015