%I #11 Jun 23 2015 00:52:52

%S 2,18,68,182,1068,1068,32318,280182,280182,3626068,23157318,120813568,

%T 1097376068,1097376068,11109655182,49925501068,355101282318,

%U 355101282318,15613890344818,15613890344818,365855836217682,2273204469030182,2273204469030182,49956920289342682

%N a(n) is the unique even-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 even residue. (The odd residues are in A259266.)

%e If m^2+1 is divisible by 5, then m mod 5 is either 2 or 3; the even value is 2, so a(1)=2.

%e If m^2+1 is divisible by 5^2, then m mod 5^2 is either 7 or 18; the even value is 18, so a(2)=18.

%e If m^2+1 is divisible by 5^3, then m mod 5^3 is either 57 or 68; the even value is 68, so a(3)=68.

%Y Cf. A048898, A048899, A257366, A259266.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Jun 15 2015

%E More terms and additional comments from _Jon E. Schoenfield_, Jun 23 2015