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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.
1
3, 7, 57, 443, 2057, 14557, 45807, 110443, 1672943, 6139557, 25670807, 123327057, 123327057, 5006139557, 19407922943, 102662389557, 407838170807, 3459595983307, 3459595983307, 79753541295807, 110981321985443, 110981321985443, 9647724486047943, 9647724486047943
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 odd residue. (The even residues are in A258929.)
EXAMPLE
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.
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.
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Jun 23 2015
STATUS
approved