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Search: id:A128245
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| A128245 |
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Smallest of three consecutive composite numbers which sum up to prime. |
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+0
1
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| 6, 9, 12, 18, 21, 22, 35, 36, 42, 45, 51, 65, 69, 78, 82, 88, 96, 102, 111, 125, 126, 135, 138, 161, 162, 165, 166, 172, 189, 198, 209, 232, 249, 255, 256, 261, 275, 291, 292, 305, 312, 316, 329, 335, 336, 345, 348, 352, 366, 371, 382, 396, 399, 408, 429, 432
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If n is a member of this sequence, either n+1 or n+2 is prime. This suggests that the density of the sequence is roughly kn/log^2 n for some k. Counts up to 10^9 suggest k is about 5.26. [From Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 11 2009]
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FORMULA
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By Rosser's theorem, a(2n) > n log n. [From Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 11 2009]
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EXAMPLE
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6+8+9=23=A060328(1), 9+10+12=31=A060328(2), 12+14+15=41=A060328(3), 18+20+21=59=A060328(4).
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MATHEMATICA
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CompositeNext[n_]:=Module[{k=n+1}, While[PrimeQ[k], k++ ]; k]; lst={}; Do[p=n+CompositeNext[n]+CompositeNext[CompositeNext[n]]; If[ !PrimeQ[n]&&PrimeQ[p], AppendTo[lst, n]], {n, 2, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009]
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PROGRAM
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(PARI) test(n)={my(b=a+1, c); b+=isprime(b); c=b+1; c+=isprime(c); isprime(a+b+c)}; for(n=4, 1e3, if(!isprime(n)&&test(n), print1(n", "))) [From Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 11 2009]
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CROSSREFS
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Cf. A060328.
Sequence in context: A136360 A023483 A023042 this_sequence A117714 A114554 A023386
Adjacent sequences: A128242 A128243 A128244 this_sequence A128246 A128247 A128248
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), May 03 2007
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