This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259266 #6 Jun 24 2015 06:42:14 %S A259266 3,7,57,443,2057,14557,45807,110443,1672943,6139557,25670807, %T A259266 123327057,123327057,5006139557,19407922943,102662389557,407838170807, %U A259266 3459595983307,3459595983307,79753541295807,110981321985443,110981321985443,9647724486047943,9647724486047943 %N A259266 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 A259266 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 A259266 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 A259266 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 A259266 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 A259266 Cf. A048898, A048899, A257366, A258929. %K A259266 nonn %O A259266 1,1 %A A259266 _Jon E. Schoenfield_, Jun 23 2015