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Search: id:A128470
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| A128470 |
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Numbers of the form 30k+1 or possible upper bounds of twin primes pairs ending in 1. |
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+0
10
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| 1, 31, 61, 91, 121, 151, 181, 211, 241, 271, 301, 331, 361, 391, 421, 451, 481, 511, 541, 571, 601, 631, 661, 691, 721, 751, 781, 811, 841, 871, 901, 931, 961, 991, 1021, 1051, 1081, 1111, 1141, 1171, 1201, 1231, 1261, 1291, 1321, 1351, 1381, 1411, 1441, 1471
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For a 30k+r "wheel", k > 0, r = 1, 13, 19 are the only possible values that can form an upper bound of a twin prime pair. The 30k+r wheel gives the sequence 1, 7, 11, 13, 17, 19, 23, 29 31, 37, 41, 43, 47, 49, 53, 59 .. which is frequently used in prime number sieves to skip multiples of 2, 3, 5. The fact that subtracting 2 from 30k+7, 11, 17, 23 will gives us a multiple of 3 or 5 precludes these numbers from being an upper bound of a twin prime pair. This leaves us with r = 1, 13, 19 for k>0 as the only possible cases to form an upper bound of a twin prime pair. 1, 13, 19 concludes the 6 numbers of the 8 number wheel that can form part of a twin prime pair.
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LINKS
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Counting Twin Primes
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EXAMPLE
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61 = 30*2 + 1, the upper part of the twin prime pair 59,61.
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MAPLE
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with(finance):seq(add(cashflows([10, 10, 10], 0 ), k=1..n)+1, n=0..49); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
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PROGRAM
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(PARI) g(n) = forstep(x=1, n, 30, print1(x", "))
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CROSSREFS
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A161700, A005408, A016813, A016921, A017281, A017533, A158057, A161705, A161709, A161714. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Sequence in context: A073650 A078562 A054804 this_sequence A132230 A136066 A114991
Adjacent sequences: A128467 A128468 A128469 this_sequence A128471 A128472 A128473
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), May 06 2007
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