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

1,1

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.

Links

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

Example

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

Mathematica

(* copied directly from A073919 with only a sign change *) ptns[n_, 0] := If[n==0, {{}}, {}]; ptns[n_, k_] := Module[{r}, If[n<k, Return[{}]]; ptns[n, k] = 1 + Union@@ Table[ PadRight[ #, k] &/ @ ptns[n-k, r], {r, 0, k}]]; a[n_] := Module[{i, l, v}, v=Infinity; For[i=n, True, i++, l=(Times@@ Prime /@ # &)/@ ptns[i, n]; If[ Min @@ l > v, Return[v]]; minp = Min@@ Select[l - 1, ProvablePrimeQ]; If[minp < v, v = minp]]] (* First do <<NumberTheory`PrimeQ`. ptns[n, k] is list of partitions of n into exactly k parts *) (* appended by Robert G. Wilson v *) Array[a, 32] (* Robert G. Wilson v, Jul 21 2011 *)

Crossrefs

Cf. A073919, A098026, A073918.

Sequence in context: A127581 A372685 A278477 * A061712 A059661 A214704

Adjacent sequences: A118880 A118881 A118882 * A118884 A118885 A118886

Keyword

nonn

Author

Rick L. Shepherd, May 03 2006

Extensions

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

Status

approved