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Search: id:A105399
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| A105399 |
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Largest prime <= numbers of the form 6k+3 (duplicates removed). |
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+0
6
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| 3, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 223, 229, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 313, 317, 331, 337, 349, 353, 359, 367, 373, 379, 383, 389
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Apart from the initial 3, the same as A049591. [Proof from T. Khovanova, Jan 23 2008: True for primes up to 5 by inspection. Higher primes must be of the form 6k+1 or 6k+5 since 6k+2 and 6k+4 are divisible by 2 and 6k+3 is divisible by 3. So searching the prime p backwards from the composite, odd 6k+3 in steps of 2 implies that p+2, skipped during that scan, is composite. So p is not in A001359 but in A049591.] - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 28 2008
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EXAMPLE
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7 is in the sequence because 7 is the largest prime < 9=6*1+3.
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MATHEMATICA
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pp[n_] := Block[{k = n}, While[ ! PrimeQ[k], k-- ]; k]; Union[Table[pp[6n + 3], {n, 0, 65}]] (*Chandler*)
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CROSSREFS
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Cf. A106002.
Cf. A049591.
Sequence in context: A034021 A038978 A133387 this_sequence A133261 A113911 A051635
Adjacent sequences: A105396 A105397 A105398 this_sequence A105400 A105401 A105402
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KEYWORD
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easy,nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), May 01 2005
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EXTENSIONS
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Edited, corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 17 2006
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