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%I #37 Sep 11 2022 22:16:59
%S 1,49,121,169,241,289,361,409,481,529,601,649,721,769,841,889,961,
%T 1009,1081,1129,1201,1249,1321,1369,1441,1489,1561,1609,1681,1729,
%U 1801,1849,1921,1969,2041,2089,2161,2209,2281,2329,2401,2449,2521,2569,2641,2689
%N Numbers congruent to {1,49} mod 120.
%C 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.
%H Bruno Berselli, <a href="/A227863/b227863.txt">Table of n, a(n) for n = 1..1000</a>
%H Gary W. Croft, <a href="http://www.primesdemystified.com/twinprimes">Twin Primes Demystified</a>
%H Gary W. Croft, <a href="http://www.primesdemystified.com/Distribution_of_Squares_Modulo_120.jpg">Matrix Demonstrating Distribution of Squares Congruent to {1,49} mod 120</a>
%H Gary W. Croft, <a href="http://www.primesdemystified.com/Squares_Distribution_1and49_Mod120.jpg">Matrix: square roots of squares congruent to {1,49} mod 120</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F G.f.: x*(1 + 48*x + 71*x^2)/((1 + x)*(1 - x)^2). [_Bruno Berselli_, Nov 04 2013]
%F a(n) = 60*n - 6*(-1)^n - 65. [_Bruno Berselli_, Nov 04 2013]
%F E.g.f.: 71 + (60*x - 65)*exp(x) - 6*exp(-x). - _David Lovler_, Sep 10 2022
%t Table[60 n - 6 (-1)^n - 65, {n, 50}] (* _Bruno Berselli_, Nov 04 2013 *)
%o (PARI) a(n)=n\2*120+[-71,1][n%2+1] \\ _Charles R Greathouse IV_, Aug 26 2014
%Y Cf. A000040, A001248, A007775.
%K nonn,easy
%O 1,2
%A _Gary Croft_, Nov 01 2013
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