A374584 - OEIS

A374584

Numbers k such that 7*k + 2 is a square.

1, 2, 14, 17, 41, 46, 82, 89, 137, 146, 206, 217, 289, 302, 386, 401, 497, 514, 622, 641, 761, 782, 914, 937, 1081, 1106, 1262, 1289, 1457, 1486, 1666, 1697, 1889, 1922, 2126, 2161, 2377, 2414, 2642, 2681, 2921, 2962, 3214, 3257, 3521, 3566, 3842, 3889

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..48.

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

FORMULA

a(n) = (A047341(n)^2 - 2)/7. - Amiram Eldar, Aug 12 2024

From Elmo R. Oliveira, Apr 11 2026: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5.

G.f.: x*(1 + x + 10*x^2 + x^3 + x^4)/((1 - x)^3*(1 + x)^2). (End)

MATHEMATICA

((Table[7*n + {3, 4}, {n, 0, 23}] // Flatten)^2 - 2)/7 (* Amiram Eldar, Aug 12 2024 *)

PROG

(Magma) [k: k in [0..4000] | IsSquare(7*k + 2)];

CROSSREFS

The numbers k such that (m + (9-m)*k) is a square: A000217 (m = 1), this sequence (m = 2), A003154 (m = 3), A195162 (m = 4), A028387 (m = 5), A100536 (m = 6), A059993 (m = 7), A028884 (m = 8).

Cf. A047341.

Sequence in context: A367461 A278975 A096508 * A355169 A108029 A212048

Adjacent sequences: A374581 A374582 A374583 * A374585 A374586 A374587

KEYWORD

nonn,easy,changed

AUTHOR

Juri-Stepan Gerasimov, Aug 12 2024

STATUS

approved