

A072325


Number of even numbers that cannot be expressed as the difference pq of two odd primes q < p <= prime(n).


2



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
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OFFSET

2,30


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.


LINKS

Table of n, a(n) for n=2..106.
Eric Weisstein's World of Mathematics, Cluster Primes


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.


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


CROSSREFS

Cf. A038133, A038134.
Sequence in context: A319581 A331302 A062977 * A294929 A076948 A255309
Adjacent sequences: A072322 A072323 A072324 * A072326 A072327 A072328


KEYWORD

easy,nonn


AUTHOR

T. D. Noe, Jul 15 2002, Nov 19 2006


STATUS

approved



