A330428 Smallest prime p such that both nearest primes up and down are farther away than n*log(p).

5, 211, 38501, 413353, 10938023, 142414669, 163710121, 8835528511, 31587561361, 343834606051, 1480975873513, 26923643849953

Offset

1,1

Comments

For these numbers, the name "Lowest Frogger Primes" LFP(n) is suggested because (frog) jumps with a length greater than n times the local average are required to bridge the gaps (logs).

Links

Table of n, a(n) for n=1..12.

Prog

(PARI) {my(npp=2, np=3, n=1); forprime(p=5, 10^9, my(d=log(p)*n); if(np-npp>d&&p-np>d, print(np, ", "); n++); npp=np; np=p)} \\ Hugo Pfoertner, Dec 14 2019

Crossrefs

Cf. A288908 (with 1*log(P)), A330426 (with 2*log(P)), A330427 (with 3*log(P)).

Cf. A023186, A120937.

Sequence in context: A203470 A165208 A293652 * A048433 A270870 A144796

Adjacent sequences: A330425 A330426 A330427 * A330429 A330430 A330431

Keyword

nonn,more,hard

Author

Steven M. Altschuld, Dec 14 2019

Extensions

a(5)-a(9) from Hugo Pfoertner, Dec 14 2019

a(10) from Hugo Pfoertner, Dec 16 2019

a(11)-a(12) from Giovanni Resta, Dec 19 2019

Status

approved