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Search: id:A100564
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| A100564 |
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Normal sequence of primes with p(1) = 3. A sequence {p(1), p(2), p(3), ... } is called a "normal sequence of primes" if p(1) is prime and if for every n > 1 p(n) is the smallest prime greater than p(n-1) such that the primes p(1), p(2), ..., p(n-1) are not divisors of p(n)-1. The existence of the primes p(n) is guaranteed by Dirichlet's theorem on primes in arithmetic progressions. |
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| 3, 5, 17, 23, 29, 53, 83, 89, 113, 149, 173, 197, 257, 263, 269, 293, 317, 353, 359, 383, 389, 419, 449, 467, 479, 503, 509, 557, 563, 569, 593, 617, 653, 659, 677, 683, 773, 797, 809, 827, 857, 863, 887, 947, 977, 983, 1049, 1097, 1109, 1217, 1223, 1229, 1283
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Erick Wong, Computations on Normal Families of Primes.
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EXAMPLE
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p(2) = 5 because p(1) = 3 is not a divisor of 4 = 5 - 1.
p(3) = 17 because p(1) = 3 is a divisor of 6 and 12 (so 7 and 13 are not possible for p(3)); p(2) = 5 is a divisor of 10 (so 11 is not possible for p(3)), but p(1) = 3 and p(2) = 5 both not divisors of 16 = 17 - 1.
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MATHEMATICA
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a[1] = 3; a[n_] := a[n] = Block[{k = PrimePi[a[n - 1]] + 1, t = Table[a[i], {i, n - 1}]}, While[ Union[ Mod[ Prime[k] - 1, t]][[1]] == 0, k++ ]; Prime[k]]; Table[ a[n], {n, 53}] (from Robert G. Wilson v Dec 04 2004)
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CROSSREFS
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Adjacent sequences: A100561 A100562 A100563 this_sequence A100565 A100566 A100567
Sequence in context: A027699 A069687 A079017 this_sequence A024862 A025106 A079649
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KEYWORD
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nonn
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AUTHOR
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Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Nov 28 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2004
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