A224908 Given n-th prime p, a(n)=number of primes of the form p+q+1 where q is any prime < p.

0, 0, 0, 2, 2, 2, 3, 3, 5, 5, 3, 4, 7, 4, 7, 8, 11, 5, 6, 9, 4, 7, 12, 14, 8, 11, 7, 13, 10, 12, 9, 15, 15, 12, 19, 9, 8, 8, 20, 19, 24, 11, 16, 11, 18, 15, 9, 13, 21, 14, 24, 27, 11, 26, 24, 26, 32, 13, 12, 21, 14, 28, 19, 27, 14, 26, 14, 14, 29, 24, 26, 39

Offset

1,4

Comments

Conjecture: a(n)>0 for all n>3. - Dmitry Kamenetsky, Feb 09 2017

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

For n=5, p=11, there are a(5)=2 solutions from 11+5+1=17 and 11+7+1=19.

Mathematica

Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p + Prime[i] + 1], c = c + 1]; i++]; c, {n, 72}]
Table[p = Prime[n] + 1; Sum[If[PrimeQ[p + Prime[i]], 1, 0], {i, 1, n - 1}], {n, 72}] (* Zak Seidov, Apr 19 2013 *)
Table[Count[Prime[n]+Prime[Range[n-1]]+1, _?PrimeQ], {n, 80}] (* Harvey P. Dale, Mar 03 2024 *)

Prog

(PARI) for(n = 1, 72, q = prime (n) + 1; print1 (sum (i = 1, n - 1, isprime (q + prime (i))) ", "))\\ Zak Seidov, Apr 19 2013

Crossrefs

Cf. A210481, A224748.

Sequence in context: A295630 A029147 A228571 * A029097 A210955 A051697

Adjacent sequences: A224905 A224906 A224907 * A224909 A224910 A224911

Keyword

nonn

Author

Jayanta Basu, Apr 19 2013

Status

approved