A224748 - OEIS

%I #16 Nov 04 2020 13:07:24

%S 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,

%T 10,9,15,7,19,17,18,10,8,8,25,12,17,12,18,29,23,12,21,12,15,28,18,11,

%U 11,12,32,25,19,22,14,29,17,27,14,40,36,18,29,16,13

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

%C Conjecture: a(n)>0 for all n>2. - _Dmitry Kamenetsky_, Feb 09 2017

%H Alois P. Heinz, <a href="/A224748/b224748.txt">Table of n, a(n) for n = 1..10000</a>

%p a:= n-> add(`if`(isprime(ithprime(n)+ithprime(i)-1), 1, 0), i=1..n-1):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Apr 18 2013

%t Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p + Prime[i] - 1], c = c + 1]; i++]; c, {n, 72}]

%t Table[Count[Prime[n]+Prime[Range[n-1]]-1,_?PrimeQ],{n,80}] (* _Harvey P. Dale_, Nov 04 2020 *)

%Y Cf. A072669, A210481, A224908.

%K nonn

%O 1,5

%A _Jayanta Basu_, Apr 17 2013