A269594 a(n) = (A269590(n)^2 + 4)/5^n, n >= 0.

4, 4, 8, 104, 212, 313, 11645, 2329, 73757, 160772, 646925, 129385, 25877, 49838696, 2503218301, 16177487972, 18226737365, 3645347473, 2526514341077, 2510040201736, 43137313790909, 136233128831473, 1960924754787877, 1733911367978596, 27260145118408781

Offset: 0

Author

Wolfdieter Lang, Mar 02 2016

Keywords

• nonn
• easy

Comments

a(n) is an integer because b(n) = A269590(n) satisfies b(n)^2 + 4 == 0 (mod 5^n), n>=0.

See A268922 for details and references.

Examples

			a(0) = (0 + 4)/1 = 4.
a(4)= (364^2 + 4)/5^4 = 212.
		

Links

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

Crossrefs

Cf. A268922, A269590, A269593 (companion).

Programs

PARI

b(n) = if (n==0, 0, 5^n - truncate(sqrt(-4+O(5^(n)))));
a(n) = (b(n)^2 + 4)/5^n; \\ Michel Marcus, Mar 24 2016

Formula

a(n) = (b(n)^2 + 4)/5^n, n>=0, with b(n) = A269590(n).

Extensions

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