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Search: id:A059767
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| A059767 |
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Initial (unsafe) primes of Cunningham chains of first type with length exactly 7. |
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+0
2
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| 1122659, 2164229, 2329469, 10257809, 10309889, 12314699, 14030309, 14145539, 19099919, 23103659, 24176129, 28843649, 37088729, 38199839, 42389519, 49160099, 50785439, 52554569, 62800169, 68718059, 85864769, 88174049
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Special primes from A059453.
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REFERENCES
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).
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FORMULA
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p primes, (2^k)*p+(2^k)-1 is prime too for k=0, 1, 2, 3, 4, 5, 6 and is composite for k=-1 and k=7.
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EXAMPLE
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C7 prime chain is generated from prime a(10)=24176129 with 2p+1 iteration: 24176129,48352259,96704519,193409039,386818079,773636159,1547272319,3094544639.
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MATHEMATICA
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Transpose[Select[{#, Length[NestWhileList[2#+1&, #, PrimeQ]]-1}&/@ Prime[Range[PrimePi[24177000]]], #[[2]]>6&]][[1]]
Select[Prime[Range[10^6]], PrimeQ[a1=2*#+1]&&PrimeQ[a2=2*a1+1]&&PrimeQ[a3=2*a2+1]&&PrimeQ[a4=2*a3+1]&&Prime\ Q[a5=2*a4+1]&&PrimeQ[a6=2*a5+1] &] (from Vladimir Orlovsky (4vladimir(AT)gmail.com), May 01 2008)
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CROSSREFS
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Cf. A023272, A023302, A023330, A005602, A007700 A005384, A005385, A059452-A059455.
Sequence in context: A038449 A059121 A116175 this_sequence A069583 A109209 A100365
Adjacent sequences: A059764 A059765 A059766 this_sequence A059768 A059769 A059770
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 21 2001
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EXTENSIONS
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Corrected and extended by Harvey P. Dale (hpd1(AT)nyu.edu), Jul 10 2002
Added more terms. Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 17 2009
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