A113293 First differences of Lucas 3-step numbers.

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

Offset: 1

Author

Jonathan Vos Post, Oct 23 2005

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A000040, A001358, A001644, A113188-A113194, A113238, A113239, A113244.

Formula

{a(n)} = { | A001644(i) - A001644(j) | such that i>=j}