OFFSET
1,1
FORMULA
a(n) ~ n^(3/2) as n -> oo.
Limit_{N->oo} (Sum_{n=2..N} log(a(n))) / (Sum_{n=2..N} log(n)) = 3/2.
EXAMPLE
a(1) = 11 since 11 is the first prime for which we find the only prime 13 between 11 and 11+1*log(11)=13.39.. .
a(2) = 37 since 37 is the second prime for which we find the two primes 41 and 43 between 37 and 37+2*log(37)=44.22.. .
a(9) = 137 since 137 is the 9th prime (>= a(8)) for which we find 9 primes between 137 and 137+9*log(137)~181.29.
PROG
(PARI) Pdeb=2; for(K=1, 40, forprime(P=Pdeb, 40^2, AR=P+K*log(P); NPR=primepi(AR)-primepi(P); if(NPR==K, print1(P, ", "); Pdeb=P; break())));
CROSSREFS
Cf. A381293.
KEYWORD
nonn,new
AUTHOR
Alain Rocchelli, Feb 21 2025
STATUS
approved