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Search: id:A035789
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| A035789 |
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Let P1,P2,..,P6 be any 6 consecutive primes. The sequence consists of those values of P3 for which P2-P1>2, P4-P3=2 and P6-P5>2. |
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7
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| 29, 41, 59, 71, 227, 239, 269, 281, 311, 347, 461, 521, 569, 599, 617, 641, 659, 857, 881, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1607, 1619, 1667, 1697, 1721, 1787, 1997, 2027, 2141, 2237, 2267, 2309, 2339, 2381, 2549, 2591, 2657, 2687
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Lesser of lonely twin primes.
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REFERENCES
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Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Nov. 19 1998.
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LINKS
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Hugo Pfoertner, Consecutive pairs of twin primes. FORTRAN program.
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EXAMPLE
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The first lonely twin primes (A069453) are 29,31 (23 and 37 are non-twin), 41,43 (37 and 47 are non-twin), 59,61 (53 and 67 are non-twin). Of these, the lesser twins are 29,41,59, so this is how the sequence begins.
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MATHEMATICA
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PrimeNext[n_]:=Module[{k}, k=n+1; While[ !PrimeQ[k], k++ ]; k]; PrimePrev[n_]:=Module[{k}, k=n-1; While[ !PrimeQ[k], k-- ]; k]; lst={}; Do[p=Prime[n]; If[ !PrimeQ[p-2]&&!PrimeQ[p+4]&&PrimeQ[p+2]&&!PrimeQ[PrimePrev[p]-2]&&!PrimeQ[PrimeN\ ext[p+2]+2], AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 22 2009]
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CROSSREFS
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Cf. A035790, A035791, A035792, A035793, A035794, A035795, A087641.
Cf. A069453, A069455.
Sequence in context: A161616 A027343 A069454 this_sequence A080899 A157141 A107218
Adjacent sequences: A035786 A035787 A035788 this_sequence A035790 A035791 A035792
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KEYWORD
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nonn
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AUTHOR
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Randall Rathbun, Nov 30 1998
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EXTENSIONS
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Edited by Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 15 2003
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