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

1,1

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A001222, A023595, A072055, A072059.

Sequence in context: A180003 A211874 A262830 * A106912 A099629 A092836

Adjacent sequences: A072057 A072058 A072059 * A072061 A072062 A072063

Keyword

nonn

Author

Reinhard Zumkeller, Jun 11 2002

Extensions

More terms from Don Reble, Apr 15 2003

Status

approved