A224793 Least prime p which generates exactly n primes of the form p+q-1 where q < p is prime, or 0 if (conjecturally) no such p exists.

2, 5, 11, 13, 47, 41, 31, 107, 43, 73, 131, 61, 191, 97, 293, 139, 353, 127, 163, 151, 0, 229, 283, 223, 659, 181, 929, 313, 241, 211, 367, 701, 271, 397, 379, 457, 337, 1031, 1259, 607, 331, 463, 643, 613, 1409, 733, 911, 1091, 541, 1997, 421, 727, 709, 673

Offset: 0

Author

Jayanta Basu, Apr 18 2013

Keywords

• nonn

Comments

a(n) = 0 for n = 20, 165, 467, ... . Do there exist infinitely many such values of n?

These values of 0 are all conjectural. - Robert Israel, Apr 28 2021

Examples

			a(1) = 5 since 5 is the least prime that generates exactly one prime 7=5+3-1 of the given form. Again a(3) = 13 since 13 generates exactly 3 primes 17=13+5-1, 19=13+7-1 and 23=13+11-1 of the given form.
		

Crossrefs

Cf. A072669, A224748.

Programs

Mathematica

Cn[n_] := Module[{c}, p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p + Prime[i] - 1], c = c + 1] i++]; c]; t = {};
Do[p = 0; j = 0; While[++j < 2000 && p != 1, If[Cn[j] == k, AppendTo[t, Prime[j]]; p = 1, p = 0]]; If[p == 0, AppendTo[t, 0]], {k, 0, 200}]; t

Extensions

Definition clarified by Robert Israel, Apr 28 2021