A335737 a(n) is the smallest prime p such that 2p+3q and 3p+2q are n-almost primes, where q is next prime after p.

5, 47, 139, 2521, 77269, 631459, 6758117, 33059357, 7607209367, 173030234371, 152129921851

Offset: 1

Author

Zak Seidov, Jun 20 2020

Keywords

• nonn
• more

Examples

			Both 2*5+3*7 = 31 and 3*5 +2*7 = 29 are primes.
Both 2*47+3*53 = 253 = 11*23 and 3*47+2*53 = 247 = 13*19 are semiprimes.
		

Crossrefs

Cf. A000040, A001358, A014612, A014613, A014614, A078840.

Programs

Mathematica

m = 6; s = Table[0, {m}]; p = 2; c = 0; While[c < m, q = NextPrime[p]; If[(o = PrimeOmega[2 p + 3 q]) ==  PrimeOmega[ 3 p + 2 q] && o <= m && s[[o]] == 0, c++; s[[o]] = p]; p = q]; s (* Amiram Eldar, Jun 23 2020 *)

PARI

for(n=1,8,my(p=2); forprime(q=3, oo, my(pq=2*p+3*q, qp=3*p+2*q); if(bigomega(pq)==n, if(bigomega(qp)==n, print1(p, ", "); break));p=q)) \\ Hugo Pfoertner, Jun 24 2020

Extensions

a(10)-a(11) from Amiram Eldar, Jun 23 2020