A118883 Smallest prime p with bigomega(p+1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity).

2, 3, 7, 23, 31, 223, 127, 383, 1151, 3583, 5119, 6143, 8191, 129023, 73727, 245759, 131071, 917503, 524287, 5505023, 10616831, 14680063, 18874367, 109051903, 169869311, 654311423, 738197503, 2264924159, 2818572287, 3758096383, 2147483647, 24159191039

Offset: 1

Author

Rick L. Shepherd, May 03 2006

Keywords

• nonn

Comments

Equivalently, smallest prime p such that p+1 is an n-almost prime. For smallest prime p such that p+1 is a squarefree n-almost prime, see A098026.

Examples

			a(4) = 23 because 23 is prime and 23+1 = 2*2*2*3 has 4 prime factors (24 is a 4-almost prime).
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..421

Crossrefs

Cf. A073919, A098026, A073918.

Programs

Mathematica

(* copied directly from A073919 with only a sign change *) ptns[n_, 0] := If[n==0, {{}}, {}]; ptns[n_, k_] := Module[{r}, If[n v, Return[v]]; minp = Min@@ Select[l - 1, ProvablePrimeQ]; If[minp < v, v = minp]]] (* First do <Robert G. Wilson v *) Array[a, 32] (* Robert G. Wilson v, Jul 21 2011 *)

PARI

almost_primes(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, listput(list, m*q)), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 2, n)));
a(n) = my(x=2^n, y=2*x); while(1, my(v=almost_primes(x, y, n)); for(k=1, #v, if(isprime(v[k]-1), return(v[k]-1))); x=y+1; y=2*x); \\ Daniel Suteu, Jan 07 2025

Extensions

a(26)-a(32) from Donovan Johnson, Feb 02 2011