1,2

The 7th-order linear recurrence A104622 (heptanacci-Lucas numbers) is a generalization of the Lucas sequence A000032. T. D. Noe and I have noted that the heptanacci-Lucas numbers have many more primes than the corresponding heptanacci (see A104414) which he found has only the first 3 primes that I identified through the first 5000 values, whereas these heptanacci-Lucas numbers have 17 primes among the first 100 values. For semiprimes in heptanacci-Lucas numbers, see A104623.

Mario Catalani, "Polymatrix and Generalized Polynacci Numbers", arXiv:math.CO/0210201 v1, Oct 14 2002

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.

Prime values of the heptanacci-Lucas numbers, which are defined by: a(0) = 7, a(1) = 1, a(2) = 3, a(3) = 7, a(4) = 15, a(5) = 31, a(6) = 63, for n > 6: a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7).

A104621(0) = 7,

A104621(2) = 3,

A104621(3) = 7,

A104621(5) = 31,

A104621(7) = 127,

A104621(10) = 983,

A104621(17) = 122401,

A104621(24) = 15231991,

a[0] = 7; a[1] = 1; a[2] = 3; a[3] = 7; a[4] = 15; a[5] = 31; a[6] = 63; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4] + a[n - 5] + a[n - 6] + a[n - 7]; Do[ If[ PrimeQ[ a[n]], Print[n]], {n, 5000}] (from Robert G. Wilson v Mar 17 2005)

Cf. A000032, A001644, A073817, A074048, A074584, A104414, A104576, A104577, A104621, A104623.

Sequence in context: A033068 A052011 A005468 this_sequence A033843 A075657 A039711

Adjacent sequences: A104619 A104620 A104621 this_sequence A104623 A104624 A104625

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 17 2005

More terms from T. D. Noe (noe(AT)sspectra.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 17 2005