Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Jan 02 2016 12:30:30
%S 0,2,3,5,7,10,17,24,25,26,28,38,40,49,62,79,89,114,140,145,182,248,
%T 353,437,654,702,784,921,931,986,1206,2136,2137,3351,5411,13264,13757,
%U 16348,27087,27160
%N Indices of prime values of heptanacci-Lucas numbers A104621.
%C 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.
%H Mario Catalani, <a href="http://arxiv.org/abs/math.CO/0210201">Polymatrix and Generalized Polynacci Numbers</a>, arXiv:math.CO/0210201 v1, Oct 14 2002
%H Tony D. Noe and Jonathan Vos Post, <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. of Integer Sequences, Vol. 8 (2005), Article 05.4.4
%F 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).
%e A104621(0) = 7,
%e A104621(2) = 3,
%e A104621(3) = 7,
%e A104621(5) = 31,
%e A104621(7) = 127,
%e A104621(10) = 983,
%e A104621(17) = 122401,
%e A104621(24) = 15231991.
%t 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}] (* _Robert G. Wilson v_, Mar 17 2005 *)
%t Flatten[Position[LinearRecurrence[{1,1,1,1,1,1,1},{7,1,3,7,15,31,63},28000],_?PrimeQ]]-1 (* _Harvey P. Dale_, Jan 02 2016 *)
%Y Cf. A000032, A001644, A073817, A074048, A074584, A104414, A104576, A104577, A104621, A104623.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Mar 17 2005
%E More terms from _T. D. Noe_ and _Robert G. Wilson v_, Mar 17 2005