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Search: id:A128467
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| A128467 |
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Numbers of the form 30k+11 or possible lower bounds of twin primes pairs ending in 1. |
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1
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| 11, 41, 71, 101, 131, 161, 191, 221, 251, 281, 311, 341, 371, 401, 431, 461, 491, 521, 551, 581, 611, 641, 671, 701, 731, 761, 791, 821, 851, 881, 911, 941, 971, 1001, 1031, 1061, 1091, 1121, 1151, 1181, 1211, 1241, 1271, 1301, 1331, 1361, 1391, 1421, 1451
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For a 30k+r "wheel", r = 11,17,29 are the only possible values that can form a a lower twin prime pair. The 30k+r wheel gives the recurrence 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 adding 2 to 30k+1,7,13,19,23 will gives us a multiple of 3 or 5, precludes these numbers from being a lower member of a twin prime pair. This leaves us with r = 11,17,29 as the only possible cases to form a lower bound of a twin prime pair.
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FORMULA
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O.g.f.: (11+19*x)/(-1+x)^2 = 19/(-1+x)+30/(-1+x)^2. a(n) = 30*n+11. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
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EXAMPLE
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41 = 30*1 + 11, the lower part of the twin prime pair 41,43.
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PROGRAM
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(PARI) g(n) = forstep(x=11, n, 30, print1(x", "))
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CROSSREFS
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Sequence in context: A040170 A085564 A109982 this_sequence A132232 A031389 A097991
Adjacent sequences: A128464 A128465 A128466 this_sequence A128468 A128469 A128470
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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 05 2007
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