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A164097 Numbers n such that 6n + 7 is a perfect square. 2
3, 7, 19, 27, 47, 59, 87, 103, 139, 159, 203, 227, 279, 307, 367, 399, 467, 503, 579, 619, 703, 747, 839, 887, 987, 1039, 1147, 1203, 1319, 1379, 1503, 1567, 1699, 1767, 1907, 1979, 2127, 2203, 2359, 2439, 2603, 2687, 2859, 2947, 3127, 3219, 3407, 3503, 3699 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The entries are prime, or divisible by 3, or divisible by prime of the form 3*m+1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

Contribution from R. J. Mathar, Aug 26 2009: (Start)

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

G.f.: x*(-3-4*x-6*x^2+x^4)/((1+x)^2*(x-1)^3).

a(n) = 3*(2*n-1+2*n^2)/4 -(-1)^n*(1+2*n)/4 = A062717(n+1)-1. (End)

MATHEMATICA

Select[Range[4000], IntegerQ[Sqrt[6 # + 7 ]] &] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {3, 7, 19, 27, 47}, 50] (* Harvey P. Dale, Apr 29 2011 *)

PROG

(MAGMA) [n: n in [1..4000] | IsSquare(6*n+7)]; // Vincenzo Librandi, Oct 12 2012

CROSSREFS

Cf. A104777 (the squares 6n+7).

Sequence in context: A001985 A203321 A203319 * A171140 A186452 A016046

Adjacent sequences:  A164094 A164095 A164096 * A164098 A164099 A164100

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 10 2009

EXTENSIONS

Edited by R. J. Mathar, Aug 26 2009

STATUS

approved

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Last modified October 18 03:25 EDT 2021. Contains 348065 sequences. (Running on oeis4.)