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A055623
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First occurrence of run of primes congruent to 1 mod 4 of exactly length n.
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17
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5, 13, 89, 389, 2593, 12401, 77069, 262897, 11593, 373649, 766261, 3358169, 12204889, 18256561, 23048897, 12270077, 297387757, 310523021, 297779117, 3670889597, 5344989829, 1481666377, 2572421893, 1113443017, 121117598053, 84676452781, 790457451349, 3498519134533, 689101181569, 3289884073409
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OFFSET
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1,1
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COMMENTS
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The term "exactly" means that before the first and after the last terms of the run, the next primes are not congruent to 1 modulo 4.
Carlos Rivera's Puzzle 256 includes Jack Brennen's a(29) starting at 689101181569 to 689101182437 and asks if anyone can break that 1999 record.
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LINKS
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FORMULA
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Compute sequence of primes congruent to 1 mod 4. When first occurrence of run of exactly length n is found, add first prime to sequence.
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EXAMPLE
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a(3)=89 because here n=3 and 89 is the start of a run of exactly 3 consecutive primes congruent to 1 mod 4.
n=3: 83, 89, 97, 101, 103 are congruent to 3, 1, 1, 1, 3 modulo 4. So a(3) = 89.
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MATHEMATICA
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nn = 10; t = Table[0, {nn}]; found = 0; p = 1; cnt = 0; While[found < nn, p = NextPrime[p]; If[Mod[p, 4] == 1, cnt++, If[0 < cnt <= nn && t[[cnt]] == 0, t[[cnt]] = NextPrime[p, -cnt]; found++]; cnt = 0]]; t (* T. D. Noe, Jun 21 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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