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

1,1

Links

Table of n, a(n) for n=1..13.

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

Example

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.

Prog

(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

Crossrefs

Cf. A046869, A028388, A096473.

Sequence in context: A270931 A241629 A273539 * A270019 A179567 A362337

Adjacent sequences: A095921 A095922 A095923 * A095925 A095926 A095927

Keyword

nonn,more

Author

Enoch Haga and Farideh Firoozbakht, Jul 12 2004

Extensions

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

Status

approved