A303436 - OEIS

%I #15 Apr 26 2018 17:37:16

%S 2,3,5,7,11,13,17,19,23,31,37,43,47,53,71,79,97,107,157,191,223,431,

%T 499,673,1151,1213,2591,51199,139967,472391,703123,786431,995327,

%U 57395627,63700991,169869311,4076863487,10871635967

%N Primes p such that all the composite numbers between p and its next prime have no more than 2 distinct prime factors.

%C Supersequence of A078883. Terms that are not there: 2, 7, 13, 19, 23, 31, 37, 43, 47, 53, 79, 97, 157, 223, 499, 673, 1213, 51199, 703123, ...

%C 5*10^11 < a(39) <= 2348273369087. - _Giovanni Resta_, Apr 26 2018

%e 157 is in the sequence since it is a prime, and the composite numbers between it and its next prime, 163, have only 2 distinct prime factors: 158 = 2*79, 159 = 3*53, 160 = 2^5*5, 161 = 7*23, and 162 = 2*3^4.

%t b[n_] := Max[Map[PrimeNu, Range[n + 1, NextPrime[n] - 1]]]; c[n_] := b[Prime[n]]; a={}; Do[If[c[n] < 3, AppendTo[a, Prime[n]]], {n, 1, 10^7}]; a

%o (PARI) isok(p) = {if (isprime(p), for(c=p+1, nextprime(p+1)-1, if (omega(c) != 2, return(0));); return (1););} \\ _Michel Marcus_, Apr 26 2018

%Y Cf. A078883.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Apr 24 2018

%E a(36) from _Michel Marcus_, Apr 26 2018

%E a(37)-a(38) from _Giovanni Resta_, Apr 26 2018