%I #17 Apr 29 2024 09:09:03
%S 5,37,211,251,32467,96377,96377,5647409,12285587,202924901,3916407479,
%T 108233238469,1279155333257
%N a(n) is the smallest prime of earliest set of at least n consecutive good primes version 1 (see A046869).
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_273.htm">Puzzle 273. Consecutive 'good' primes</a>, The Prime Puzzles & Problem Connection.
%e 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.
%e 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.
%o (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
%Y Cf. A046869, A028388, A096473.
%K nonn,more
%O 1,1
%A _Enoch Haga_ and _Farideh Firoozbakht_, Jul 12 2004
%E Name clarified and a(12)-a(13) added by _Amiram Eldar_, Apr 29 2024