A072060 Smallest prime p such that 2*p+1 has n prime factors (with multiplicity).

2, 7, 13, 67, 283, 607, 1093, 12757, 22963, 49207, 482233, 1623847, 797161, 14614627, 19929037, 35872267, 150663523, 2044719247, 1355971711, 9879222469, 37773497677, 200490103057, 172595827849, 235357947067, 1176789735337, 5507375961379, 10591107618037

Offset: 1

Author

Reinhard Zumkeller, Jun 11 2002

Keywords

• nonn

Examples

			a(4)=67=A000040(19): 2*67+1 = 135 = 5*3^3, 4 factors.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001222, A023595, A072055, A072059.

Programs

PARI

generate(A, B, n) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p,ceil(A/m)), B\m, my(t=m*q); if(isprime((t-1)/2), listput(list, (t-1)/2))), forprime(q = p, sqrtnint(B\m, n), my(t=m*q); list=concat(list, f(t, q, n-1)))); list); vecsort(Vec(f(1, 3, n)));
a(n) = my(x=2^n, y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Feb 05 2023

Extensions

More terms from Don Reble, Apr 15 2003