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 A113294 First differences of Lucas 4-step numbers. 1
 1, 3, 4, 8, 11, 12, 19, 22, 23, 25, 36, 44, 47, 48, 73, 84, 92, 95, 96, 140, 165, 176, 184, 187, 188, 268, 316, 341, 352, 360, 363, 364, 517, 609, 657, 682, 693, 701, 704, 705, 998, 1174, 1266, 1314, 1339, 1350, 1358, 1361, 1362, 1923, 2264, 2440, 2532, 2580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Lucas 4-step numbers are also known as "Tetranacci Lucas numbers" or "Tetranacci numbers with different initial conditions" in A073817. Primes in this sequence are A113295. In this sequence are: 13340261 = 11 * 19 * 29 * 31 * 71 is a product of 5 distinct 2-digit primes; 95550683 = 269 * 593 * 599 is a product of 3 distinct 3-digit primes. LINKS Table of n, a(n) for n=1..54. 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)} = { | A073817(i) - A073817(j) | such that i>=j } EXAMPLE a(0) = 1 because A073817(0)-A001644(2) = 4 - 3 = 1. a(1) = 3 because A073817(3)-A001644(0) = 7 - 4 = 3. a(2) = 4 because A073817(3)-A001644(2) = 7 - 3 = 4. a(3) = 8 because A073817(4)-A001644(3) = 15 - 7 = 8. a(122) = 70000 because A073817(17)-A001644(3) = 70007 - 7 = 70000. CROSSREFS Cf. A000040, A073817, A113188-A113194, A113238, A113239, A113244, A113293, A113295. Sequence in context: A047458 A004014 A243177 * A169691 A255748 A152412 Adjacent sequences: A113291 A113292 A113293 * A113295 A113296 A113297 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Oct 23 2005 STATUS approved

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