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A072325
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Number of even numbers that cannot be expressed as the difference p-q of two odd primes q < p <= prime(n).
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,30
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COMMENTS
| If a(n)=0, then Prime[n], called a cluster prime, is in A038134. If a(n)>0 then Prime[n] is in A038133.
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LINKS
| Eric Weisstein's World of Mathematics, Cluster Primes
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EXAMPLE
| a(25)=1 because Prime[25]=97 and there is 1 even number, 88, that cannot be written as the difference of two odd primes less than or equal to 97.
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MATHEMATICA
| m=10000; n=PrimePi[m]-1; p=Table[Prime[i+1], {i, n}]; d=Table[0, {m/2}]; c=Table[0, {n}]; For[i=2, i<=n, i++, For[j=1, j<i, j++, diff=p[[i]]-p[[j]]; d[[diff/2]]++ ]; c[[i]]=Count[Take[d, (p[[i]]-3)/2], 0]]; c
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CROSSREFS
| Cf. A038133, A038134.
Sequence in context: A135468 A003196 A062977 * A076948 A086071 A089813
Adjacent sequences: A072322 A072323 A072324 * A072326 A072327 A072328
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jul 15 2002, Nov 19 2006
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