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A104622
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Indices of prime values of heptanacci-Lucas numbers A104621.
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5
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0, 2, 3, 5, 7, 10, 17, 24, 25, 26, 28, 38, 40, 49, 62, 79, 89, 114, 140, 145, 182, 248, 353, 437, 654, 702, 784, 921, 931, 986, 1206, 2136, 2137, 3351, 5411, 13264, 13757, 16348, 27087, 27160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
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REFERENCES
| 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.
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FORMULA
| 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).
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EXAMPLE
| A104621(0) = 7,
A104621(2) = 3,
A104621(3) = 7,
A104621(5) = 31,
A104621(7) = 127,
A104621(10) = 983,
A104621(17) = 122401,
A104621(24) = 15231991,
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MATHEMATICA
| 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)
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CROSSREFS
| Cf. A000032, A001644, A073817, A074048, A074584, A104414, A104576, A104577, A104621, A104623.
Sequence in context: A033068 A052011 A005468 * A033843 A075657 A039711
Adjacent sequences: A104619 A104620 A104621 * A104623 A104624 A104625
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 17 2005
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EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 17 2005
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