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A227863 Numbers congruent to {1,49} mod 120. 1
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 (list; graph; refs; listen; history; text; internal format)
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]

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: A178705 A163245 A084733 * A115557 A167718 A080665

Adjacent sequences:  A227860 A227861 A227862 * A227864 A227865 A227866

KEYWORD

nonn,easy

AUTHOR

Gary Croft, Nov 01 2013

STATUS

approved

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Last modified August 20 06:32 EDT 2017. Contains 290824 sequences.