A227863 Numbers congruent to {1,49} mod 120.

1, 49, 121, 169, 241, 289, 361, 409, 481, 529, 601, 649, 721, 769, 841, 889, 961, 1009, 1081, 1129, 1201, 1249, 1321, 1369, 1441, 1489, 1561, 1609, 1681, 1729, 1801, 1849, 1921, 1969, 2041, 2089, 2161, 2209, 2281, 2329, 2401, 2449, 2521, 2569, 2641, 2689

Offset: 1

Author

Gary Croft, Nov 01 2013

Keywords

• nonn
• easy

Comments

The squares of natural numbers not divisible by 2, 3 or 5 and therefore the squares of prime numbers >5 are confined to this sequence.

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A000040, A001248, A007775.

Programs

Mathematica

Table[60 n - 6 (-1)^n - 65, {n, 50}] (* Bruno Berselli, Nov 04 2013 *)
LinearRecurrence[{1,1,-1},{1,49,121},50] (* or *) #+{1,49}&/@(120*Range[0,30])//Flatten (* Harvey P. Dale, Jul 13 2025 *)

PARI

a(n)=n\2*120+[-71,1][n%2+1] \\ Charles R Greathouse IV, Aug 26 2014

Formula

G.f.: x*(1 + 48*x + 71*x^2)/((1 + x)*(1 - x)^2). [Bruno Berselli, Nov 04 2013]

a(n) = 60*n - 6*(-1)^n - 65. [Bruno Berselli, Nov 04 2013]

E.g.f.: 71 + (60*x - 65)*exp(x) - 6*exp(-x). - David Lovler, Sep 10 2022