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%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
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