A095924 a(n) is the smallest prime of earliest set of at least n consecutive good primes version 1 (see A046869).

5, 37, 211, 251, 32467, 96377, 96377, 5647409, 12285587, 202924901, 3916407479, 108233238469, 1279155333257

Offset: 1

Author

Enoch Haga and Farideh Firoozbakht, Jul 12 2004

Keywords

• nonn
• more

Examples

			A good prime (version 1) is a prime p = prime(n) such that prime(n)^2 > prime(n-1)*prime(n+1), so 5 is a good prime because 5 = prime(3); prime(2) = 3; prime(4) = 7 and 5^2 > 3*7.
a(11) = 3916407479 because the 11 consecutive primes 3916407479, 3916407527, 3916407569, 3916407611, 3916407653, 3916407679, 3916407697, 3916407713, 3916407727, 3916407739 and 3916407751 are good primes and 3916407479 is the smallest prime with this property.
		

Links

• Carlos Rivera, Puzzle 273. Consecutive 'good' primes, The Prime Puzzles & Problem Connection.

Crossrefs

Cf. A046869, A028388, A096473.

Programs

PARI

lista(pmax) = {my(c = 0, cmax = 0, p1 = 2, p2 = 3, p); forprime(p3 = 5, pmax, if(p2^2 > p1*p3, c++, if(c > cmax, p = p1; for(i = 1, c-1, p = precprime(p-1)); for(i = 1, c-cmax, print1(p, ", ")); cmax = c); c = 0); p1 = p2; p2 = p3);} \\ Amiram Eldar, Apr 29 2024

Extensions

Name clarified and a(12)-a(13) added by Amiram Eldar, Apr 29 2024