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 A113293 First differences of Lucas 3-step numbers. 2
 0, 2, 4, 6, 8, 10, 14, 18, 20, 28, 32, 36, 38, 50, 60, 64, 68, 70, 92, 110, 120, 124, 128, 130, 170, 202, 220, 230, 234, 238, 240, 312, 372, 404, 422, 432, 436, 440, 442, 574, 684, 744, 776, 794, 804, 808, 812, 814, 1056, 1258, 1368, 1428, 1460, 1478, 1488 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There are no primes in this sequence, except 2, as all values are odd, so all differences are even. Semiprimes include: a(3) = 4, a(4) = 6, a(6) = 10, a(7) = 14, a(13) = 38, a(26) = 202, a(35) = 422, a(44) = 794, a(54) = 1478, a(59) = 1942, a(66) = 2746, a(94) = 9326. LINKS Table of n, a(n) for n=1..55. Eric Weisstein's World of Mathematics, Lucas n-Step Number. Noe, T. D. and Post, J. V., Primes in Fibonacci n-step and Lucas n-Step Sequences." J. Integer Seq. 8, Article 05.4.4, 2005. FORMULA {a(n)} = { | A001644(i) - A001644(j) | such that i>=j} EXAMPLE a(0) = 0 because A001644(2)-A001644(0) = 3 - 3 = 0. a(1) = 2 because A001644(2)-A001644(1) = 3 - 1 = 2. a(2) = 4 because A001644(3)-A001644(2) = 7 - 3 = 4. a(3) = 6 because A001644(3)-A001644(1) = 7 - 1 = 6. a(75) = 5000 because A001644(14)-A001644(7) = 5071 - 71 = 5000. CROSSREFS Cf. A000040, A001358, A001644, A113188-A113194, A113238, A113239, A113244. Sequence in context: A220850 A151566 A160406 * A080431 A288732 A122642 Adjacent sequences: A113290 A113291 A113292 * A113294 A113295 A113296 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Oct 23 2005 STATUS approved

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