

A303436


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


0



2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 43, 47, 53, 71, 79, 97, 107, 157, 191, 223, 431, 499, 673, 1151, 1213, 2591, 51199, 139967, 472391, 703123, 786431, 995327, 57395627, 63700991, 169869311, 4076863487, 10871635967
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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, ...


LINKS



EXAMPLE

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.


MATHEMATICA

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


PROG

(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


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



