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 A229852 3*h^2, where h is an odd integer not divisible by 3. 3
 3, 75, 147, 363, 507, 867, 1083, 1587, 1875, 2523, 2883, 3675, 4107, 5043, 5547, 6627, 7203, 8427, 9075, 10443, 11163, 12675, 13467, 15123, 15987, 17787, 18723, 20667, 21675, 23763, 24843, 27075, 28227, 30603, 31827, 34347, 35643, 38307, 39675, 42483, 43923 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p = a(n)*2^k + 1 divides a composite Fermat number 2^(2^m) + 1 and p is a prime, then k is odd. More precisely, k == 1 (mod 4) if h == +/- 1 (mod 5) and k == 3 (mod 4) if h == +/- 2 (mod 5) (Krizek, Luca and Somer). REFERENCES M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001, pp. 63-65. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Wilfrid Keller, Fermat factoring status. Eric Weisstein's World of Mathematics, Fermat Number. Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA G.f.: 3*x*(1+24*x+22*x^2+24*x^3+x^4) / ((1-x)^3*(1+x)^2). a(n) = 3*A104777(n). From Colin Barker, Jan 26 2016: (Start) a(n) = 3*(18*n^2+6*(-1)^n*n-18*n-3*(-1)^n+5)/2. a(n) = 27*n^2-18*n+3 for n even. a(n) = 27*n^2-36*n+12 for n odd. (End) Sum_{n>=1} 1/a(n) = Pi^2/27 (A291050). - Amiram Eldar, Jan 02 2021 MATHEMATICA 3*Select[Range[1, 121, 2], Mod[#, 3] > 0 &]^2 (* Amiram Eldar, Jan 02 2021 *) PROG (Magma) [3*h^2 : h in [1..121 by 2] | not IsZero(h mod 3)] (PARI) forstep(h=1, 121, 2, if(!(h%3==0), print1(3*h^2, ", "))); (PARI) Vec(3*x*(1+24*x+22*x^2+24*x^3+x^4) / ((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016 CROSSREFS Cf. A000215, A204620, A291050. Sequence in context: A093183 A278380 A290774 * A265956 A189805 A230145 Adjacent sequences: A229849 A229850 A229851 * A229853 A229854 A229855 KEYWORD nonn,easy AUTHOR Arkadiusz Wesolowski, Oct 01 2013 STATUS approved

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