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Search: id:A153196
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| A153196 |
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Numbers n such that 6*n+5 and 6*n+7 are twin primes. |
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1
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| 0, 1, 2, 4, 6, 9, 11, 16, 17, 22, 24, 29, 31, 32, 37, 39, 44, 46, 51, 57, 69, 71, 76, 86, 94, 99, 102, 106, 109, 134, 136, 137, 142, 146, 169, 171, 174, 176, 181, 191, 204, 212, 214, 216, 219, 237, 241, 246, 247, 267, 269, 277, 282, 286, 297, 311, 312, 321, 324, 332
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(j) = (A001359(j+1)-5)/6.
a(j) = A002822(j)-1.
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EXAMPLE
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For n = 0, 6*n+5 = 5 and 6*n+7 = 7 are twin primes; for n = 99, 6*n+5 = 599 and 6*n+7 = 601 are twin primes.
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MAPLE
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ZL := []; for p to 1000000 do if `and`(isprime(p), isprime(p+2)) then ZL := [op(ZL), ((p+2)^2-p^2)*(1/8)] end if end do; A160273 := [seq((ZL[i+1]-ZL[i])*(1/3), i = 2 .. nops(ZL)-1)]: ListTools[PartialSums]( A160273 ); [From Stephen Crowley (crow(AT)crowlogic.net), May 24 2009]
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PROGRAM
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(MAGMA) [ n: n in [0..335] | IsPrime(6*n+5) and IsPrime(6*n+7) ];
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CROSSREFS
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Cf. A001359 (lesser of twin primes), A002822 (6n-1, 6n+1 are twin primes).
Cf. A037074 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 26 2008]
Appears to be the partial sums of A160273 which are the successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040) [From Stephen Crowley (crow(AT)crowlogic.net), May 24 2009]
Sequence in context: A164286 A054519 A038107 this_sequence A077220 A128716 A025057
Adjacent sequences: A153193 A153194 A153195 this_sequence A153197 A153198 A153199
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 20 2008
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 26 2008
Relation to partial sums of twin prime gaps [From Stephen Crowley (crow(AT)crowlogic.net), May 24 2009]
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