A100964 Smallest prime number that begins a prime gap of at least 2n.

3, 7, 23, 89, 113, 113, 113, 523, 523, 887, 1129, 1327, 1327, 1327, 1327, 1327, 1327, 9551, 15683, 15683, 15683, 15683, 19609, 19609, 19609, 19609, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 155921, 155921, 155921, 155921

Offset: 1

Author

T. D. Noe, Nov 23 2004

Keywords

• nonn

Examples

			a(5) = a(6) = a(7) = 113 because there is a gap of 14 between 113 and 127.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..775

Crossrefs

Cf. A000230, A002386, A005250, A144309.

Programs

Mathematica

k=1; Table[While[Prime[k+1]-Prime[k] < 2n, k++ ]; Prime[k], {n, 48}]

PARI

lista(pmax) = {my(k = 1, prv = 2, m = 2, kprv = 2); forprime(p = 3, pmax, k++; if(p - prv >= m, for(i = 1, (p - prv - m)/2 + 1, print1(prv, ", ")); m = p - prv + 2; kprv = k); prv = p);} \\ Amiram Eldar, Sep 06 2024

Formula

a(n) = prime(A144309(n)). - Michel Marcus, Nov 02 2013