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A072325
Number of even numbers that cannot be expressed as the difference p-q 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
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
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
Sequence in context: A331302 A062977 A357879 * A294929 A076948 A255309
KEYWORD
easy,nonn
AUTHOR
T. D. Noe, Jul 15 2002, Nov 19 2006
STATUS
approved