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Search: id:A055624
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| A055624 |
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First occurrence of run of primes congruent to 3 mod 4 of exactly length n. |
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+0
7
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| 3, 7, 739, 199, 883, 13127, 463, 36551, 39607, 183091, 4468903, 6419299, 241603, 11739307, 9177431, 95949311, 105639091, 341118307, 1800380579, 727334879, 9449915743, 1786054147, 22964264027, 54870713243, 79263248027, 454648144571, 722204126767, 1749300591127, 5070807638111, 8858854801319, 6425403612031, 113391385603
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The tern "exactly" means that before the first and after the last terms of chain, the immediate primes are not congruent to 3 modulo 4.
Carlos Rivera's Puzzle 256 includes Jack Brennan's a(24) starting at 1602195714419 to 1602195715423 and asks if anyone can break that 1999 record.
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LINKS
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J. K. Andersen, Consecutive Congruent Primes.
Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 256, Jack Brennen old records
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FORMULA
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Compute sequence of primes congruent to 3 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)=739 because here n=3 and 739 is the start of a run of exactly 3 consecutive primes congruent to 3 mod 4.
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CROSSREFS
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Cf. A092567, A055623, A055626.
Sequence in context: A101246 A056801 A092568 this_sequence A065244 A012844 A104052
Adjacent sequences: A055621 A055622 A055623 this_sequence A055625 A055626 A055627
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KEYWORD
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easy,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 05 2000
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EXTENSIONS
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More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 18 2001
More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), May 29 2006
Edited by njas, Jun 01 2006
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