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Search: id:A038134
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| A038134 |
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From a subtractive Goldbach conjecture: cluster primes. |
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+0
9
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| 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 233, 239, 241, 271, 277, 281, 283, 311, 313, 317, 353, 359, 389, 401, 421, 433
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Erdos asks if there are infinitely many primes p such that every even number <= p-3 can be expressed as the difference between two primes each <= p.
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REFERENCES
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R. Blecksmith et al., Cluster primes, Amer. Math. Monthly, 106 (1999), 43-48.
R. K. Guy, Unsolved Problems In Number Theory, section C1.
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LINKS
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T. D. Noe, Cluster primes less than 10^6; table of n, a(n) for n = 1..8287
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Goldbach conjecture
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MATHEMATICA
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m=1000; lst={}; n=PrimePi[m]-1; p=Table[Prime[i+1], {i, n}]; d=Table[0, {m/2}]; For[i=2, i<=n, i++, For[j=1, j<i, j++, diff=p[[i]]-p[[j]]; d[[diff/2]]++ ]; c=Count[Take[d, (p[[i]]-3)/2], 0]; If[c==0, AppendTo[lst, p[[i]]]]]; lst
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CROSSREFS
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Cf. A038133, A039506, A039507, A072325.
Sequence in context: A160656 A073579 A065380 this_sequence A138980 A020615 A165255
Adjacent sequences: A038131 A038132 A038133 this_sequence A038135 A038136 A038137
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), Feb 15 1999.
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