OFFSET
1,1
LINKS
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
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