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 A305862 a(n) = 384*4^n - 576*3^n + 220*2^n - 14. 2
 14, 234, 1826, 10770, 55154, 260274, 1167026, 5059890, 21442994, 89438514, 368866226, 1509026610, 6137242034, 24853275954, 100327829426, 404059098930, 1624486948274, 6522713868594, 26165182536626, 104883769004850, 420204307937714, 1682825158192434, 6737324873467826 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Bruno Berselli, Jun 15 2018: (Start) a(0) = 2*7 and a(40) = 2*232110255958477539427146457 are semiprimes. For which values of n > 40 is a(n) semiprime? For odd n, a(n) is divisible by 2*3. For n == 3 (mod 4), a(n) is divisible by 2*3*5. For n == 0 or 5 (mod 6), a(n) is divisible by 2*7. For n == 2 or 4 (mod 5), a(n) is divisible by 2*11. For n == 1 or 11 (mod 12), a(n) is divisible by 2*3*13. For n == 15 (mod 16), a(n) is divisible by 2*3*5*17^2, etc. If a(n) is divisible by 37 then it is also divisible by 3*5*7*13*19*73. (End) LINKS Takao Komatsu, On poly-Euler numbers of the second kind, arXiv:1806.05515 [math.NT], 2018, page 11 (Lemma 3.4). Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24). FORMULA G.f.: 2*(7 + 47*x - 12*x^2)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4). a(n) = 14*A000453(n+4) + 94*A000453(n+3) - 24*A000453(n+2) for n>1. - Bruno Berselli, Jun 15 2018 MATHEMATICA Table[384 4^n - 576 3^n + 220 2^n - 14, {n, 0, 30}] PROG (MAGMA) [384*4^n-576*3^n+220*2^n-14: n in [0..30]]; (PARI) a(n) = 384*4^n - 576*3^n + 220*2^n - 14; \\ Michel Marcus, Jul 03 2018 CROSSREFS Cf. A000453, A000918, A305861. Sequence in context: A079563 A230346 A280559 * A222377 A220502 A256462 Adjacent sequences:  A305859 A305860 A305861 * A305863 A305864 A305865 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jun 15 2018 STATUS approved

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Last modified October 16 11:49 EDT 2019. Contains 328056 sequences. (Running on oeis4.)