A269593 a(n) = (A268922(n)^2 + 4)/5^n, n >= 0.

4, 1, 5, 1, 109, 1460, 292, 53476, 124904, 993169, 5385572, 43930532, 239139524, 777233593, 789206948, 2256445369, 65340851012, 661111023620, 132222204724, 7745142596633, 10225443529556, 103321258570120, 20664251714024, 4562022446935993, 6246398287209928, 20888388201358465

Offset

0,1

Comments

a(n) is integer because b(n) = A268922(n) satisfies b(n)^2 + 4 == 0 (mod 5^n), n>=0.

See A268922 for details and references.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

a(n) = (b(n)^2 + 1)/5^n, n>=0, with b(n) = A268922(n).

Example

a(0) = (0 + 4)/1 = 4.
a(4) = (261^2 + 4)/5^4 = 109.

Prog

(PARI) a(n) = ((truncate(sqrt(-4+O(5^(n)))))^2 + 4)/5^n; \\ Michel Marcus, Mar 07 2016

Crossrefs

Cf. A268922, A269590, A269594 (companion sequence).

Sequence in context: A168066 A029666 A345312 * A194512 A131230 A076063

Adjacent sequences: A269590 A269591 A269592 * A269594 A269595 A269596

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 02 2016

Extensions

Terms a(21) and beyond from Andrew Howroyd, Mar 02 2020

Status

approved