

A224748


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


14



0, 0, 1, 1, 2, 3, 3, 3, 2, 3, 6, 6, 5, 8, 4, 4, 4, 11, 11, 8, 9, 11, 4, 5, 13, 9, 11, 7, 13, 5, 17, 10, 9, 15, 7, 19, 17, 18, 10, 8, 8, 25, 12, 17, 12, 18, 29, 23, 12, 21, 12, 15, 28, 18, 11, 11, 12, 32, 25, 19, 22, 14, 29, 17, 27, 14, 40, 36, 18, 29, 16, 13
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,5


COMMENTS

Conjecture: a(n)>0 for all n>2.  Dmitry Kamenetsky, Feb 09 2017


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


MAPLE

a:= n> add(`if`(isprime(ithprime(n)+ithprime(i)1), 1, 0), i=1..n1):
seq(a(n), n=1..100); # Alois P. Heinz, Apr 18 2013


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[Count[Prime[n]+Prime[Range[n1]]1, _?PrimeQ], {n, 80}] (* Harvey P. Dale, Nov 04 2020 *)


CROSSREFS

Cf. A072669, A210481, A224908.
Sequence in context: A305374 A084966 A303432 * A165494 A204916 A322225
Adjacent sequences: A224745 A224746 A224747 * A224749 A224750 A224751


KEYWORD

nonn


AUTHOR

Jayanta Basu, Apr 17 2013


STATUS

approved



