A113293 - OEIS

%I #4 Mar 30 2012 18:40:30

%S 0,2,4,6,8,10,14,18,20,28,32,36,38,50,60,64,68,70,92,110,120,124,128,

%T 130,170,202,220,230,234,238,240,312,372,404,422,432,436,440,442,574,

%U 684,744,776,794,804,808,812,814,1056,1258,1368,1428,1460,1478,1488

%N First differences of Lucas 3-step numbers.

%C 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Lucasn-StepNumber.html">Lucas n-Step Number.</a>

%H Noe, T. D. and Post, J. V., <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html">Primes in Fibonacci n-step and Lucas n-Step Sequences."</a> J. Integer Seq. 8, Article 05.4.4, 2005.

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

%e a(0) = 0 because A001644(2)-A001644(0) = 3 - 3 = 0.

%e a(1) = 2 because A001644(2)-A001644(1) = 3 - 1 = 2.

%e a(2) = 4 because A001644(3)-A001644(2) = 7 - 3 = 4.

%e a(3) = 6 because A001644(3)-A001644(1) = 7 - 1 = 6.

%e a(75) = 5000 because A001644(14)-A001644(7) = 5071 - 71 = 5000.

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

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Oct 23 2005