A258929 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.

2, 18, 68, 182, 1068, 1068, 32318, 280182, 280182, 3626068, 23157318, 120813568, 1097376068, 1097376068, 11109655182, 49925501068, 355101282318, 355101282318, 15613890344818, 15613890344818, 365855836217682, 2273204469030182, 2273204469030182, 49956920289342682

Offset

1,1

Comments

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.)

Links

Table of n, a(n) for n=1..24.

Example

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.
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.
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.

Crossrefs

Cf. A048898, A048899, A257366, A259266.

Sequence in context: A368755 A112365 A242200 * A034959 A316902 A316904

Adjacent sequences: A258926 A258927 A258928 * A258930 A258931 A258932

Keyword

nonn

Author

Jon E. Schoenfield, Jun 15 2015

Extensions

More terms and additional comments from Jon E. Schoenfield, Jun 23 2015

Status

approved