A072325 Number of even numbers that cannot be expressed as the difference p-q of two odd primes q < p <= prime(n).

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

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: A331302 A062977 A357879 * 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