Search: id:A038134
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%I A038134
%S A038134 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T A038134 101,103,107,109,113,131,137,139,151,157,163,167,173,179,181,193,197,
%U A038134 199,233,239,241,271,277,281,283,311,313,317,353,359,389,401,421,433
%N A038134 From a subtractive Goldbach conjecture: cluster primes.
%C A038134 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.
%D A038134 R. Blecksmith et al., Cluster primes, Amer. Math. Monthly, 106 (1999), 
               43-48.
%D A038134 R. K. Guy, Unsolved Problems In Number Theory, section C1.
%H A038134 T. D. Noe, <a href="b038134.txt">Cluster primes less than 10^6; table 
               of n, a(n) for n = 1..8287</a>
%H A038134 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ClusterPrime.html">Link to a section of The World of Mathematics.</
               a>
%H A038134 <a href="Sindx_Go.html#Goldbach">Index entries for sequences related 
               to Goldbach conjecture</a>
%t A038134 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
%Y A038134 Cf. A038133, A039506, A039507, A072325.
%Y A038134 Sequence in context: A160656 A073579 A065380 this_sequence A138980 A020615 
               A165255
%Y A038134 Adjacent sequences: A038131 A038132 A038133 this_sequence A038135 A038136 
               A038137
%K A038134 nonn,easy
%O A038134 1,1
%A A038134 N. J. A. Sloane (njas(AT)research.att.com).
%E A038134 More terms from Christian G. Bower (bowerc(AT)usa.net), Feb 15 1999.

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