A303436 Primes p such that all the composite numbers between p and its next prime have no more than 2 distinct prime factors.

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

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, ...

5*10^11 < a(39) <= 2348273369087. - Giovanni Resta, Apr 26 2018

Links

Table of n, a(n) for n=1..38.

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

Cf. A078883.

Sequence in context: A006514 A216286 A086983 * A334797 A229060 A219528

Adjacent sequences: A303433 A303434 A303435 * A303437 A303438 A303439

Keyword

nonn,more

Author

Amiram Eldar, Apr 24 2018

Extensions

a(36) from Michel Marcus, Apr 26 2018

a(37)-a(38) from Giovanni Resta, Apr 26 2018

Status

approved