A113294 First differences of Lucas 4-step numbers.

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

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