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

1,2

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