A113294 - OEIS

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

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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.