|
Search: id:A072325
|
|
|
| A072325 |
|
Number of even numbers that cannot be expressed as the difference p-q of two odd primes q < p <= prime(n). |
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
2,30
|
|
|
COMMENT
|
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
|
Cf. A038133, A038134.
Sequence in context: A135468 A003196 A062977 this_sequence A076948 A086071 A089813
Adjacent sequences: A072322 A072323 A072324 this_sequence A072326 A072327 A072328
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Jul 15 2002, Nov 19 2006
|
|
|
Search completed in 0.002 seconds
|
