A375352 Numbers k such that 14*k + 2 is a square.

1, 7, 23, 41, 73, 103, 151, 193, 257, 311, 391, 457, 553, 631, 743, 833, 961, 1063, 1207, 1321, 1481, 1607, 1783, 1921, 2113, 2263, 2471, 2633, 2857, 3031, 3271, 3457, 3713, 3911, 4183, 4393, 4681, 4903, 5207, 5441, 5761, 6007, 6343, 6601, 6953, 7223, 7591, 7873

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 12 2024

Keywords

• nonn
• easy

Comments

a(11) = 391 is first composite number in this sequence.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Numbers k such that (m + (16-m)*k) is a square: A204221 (m = 1), this sequence (m = 2), A001082 (m = 4), A181433 (m = 5), A273367 (m = 6), A266956 (m = 7), A056220 (m = 8), A274978 (m = 9), A028872 (m = 12), A161532 (m = 14).

Cf. A113804, A212965.

Programs

Magma

[k: k in [0..8000] | IsSquare(14*k + 2)];

Mathematica

((Table[14*n + {4, 10}, {n, 0, 23}] // Flatten)^2 - 2)/14 (* Amiram Eldar, Aug 13 2024 *)

Formula

a(n) = (A113804(n)^2 - 2)/14. - Amiram Eldar, Aug 13 2024

a(n) = 2*A212965(n-1) - 1. - Hugo Pfoertner, Aug 13 2024

E.g.f.: ((2 + x + 7*x^2)*cosh(x) + (1 - x + 7*x^2)*sinh(x) - 2)/2. - Stefano Spezia, Aug 13 2024