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Search: id:A059763
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| A059763 |
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Primes starting a Cunningham chain of the first kind of length 4. |
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+0 11
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| 509, 1229, 1409, 2699, 3539, 6449, 10589, 11549, 11909, 12119, 17159, 19709, 19889, 22349, 26189, 27479, 30389, 43649, 55229, 57839, 60149, 71399, 74699, 75329, 82499, 87539, 98369, 101399, 104369, 112919, 122099, 139439, 148829, 166739
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Initial (unsafe) primes of Cunningham chains of first type with length exactly 4. Primes in A059453 which survive as primes just three "2p+1 iterations", forming chains of exactly 4 terms.
The definition indicates each chain is exactly 4 primes long (i.e. the chain cannot be a subchain of a longer one). That's why this sequence is different from A023272 which gives also primes included in longer chains ("starting" them or not).
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LINKS
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Chris Caldwell's Prime Glossary, Cunningham chains.
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FORMULA
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{(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15} = {composite, prime, prime, prime, prime, composite}
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EXAMPLE
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1229 is here because, through 2p+1, 1229 -> 2459 -> 4919 -> 9839 and the chain ends here since 2*9839+1=11*1789 is composite.
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MAPLE
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isA059763 := proc(p) local pitr, itr ; if isprime(p) then if isprime( (p-1)/2 ) then RETURN(false) ; else pitr := p ; for itr from 1 to 3 do pitr := 2*pitr+1 ; if not isprime(pitr) then RETURN(false) ; fi ; od: pitr := 2*pitr+1 ; if isprime(pitr) then RETURN(false) ; else RETURN(true) ; fi ; fi ; else RETURN(false) ; fi ; end: for i from 2 to 100000 do p := ithprime(i) ; if isA059763(p) then printf("%d, ", p) ; fi ; od: # R. J. Mathar Jul 23 2008
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CROSSREFS
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Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, Cf. A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.
Sequence in context: A159686 A142819 A110025 this_sequence A126438 A126582 A062905
Adjacent sequences: A059760 A059761 A059762 this_sequence A059764 A059765 A059766
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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), Feb 20 2001
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2008, Aug 18 2008
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