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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] 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 A374290 A115557 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 July 19 13:28 EDT 2024. Contains 374394 sequences. (Running on oeis4.)