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

1,2

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

Gary W. Croft, Twin Primes Demystified

Gary W. Croft, Matrix Demonstrating Distribution of Squares Congruent to {1,49} mod 120

Gary W. Croft, Matrix: square roots of squares congruent to {1,49} mod 120

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

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

Mathematica

Table[60 n - 6 (-1)^n - 65, {n, 50}] (* Bruno Berselli, Nov 04 2013 *)

Prog

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

Crossrefs

Cf. A000040, A001248, A007775.

Sequence in context: A163245 A084733 A338499 * A339131 A115557 A167718

Adjacent sequences: A227860 A227861 A227862 * A227864 A227865 A227866

Keyword

nonn,easy

Author

Gary Croft, Nov 01 2013

Status

approved