A191587 Smallest prime p such that p-n is the product of exactly n distinct primes.

3, 17, 73, 1789, 6011, 1616621, 2114977, 111546443, 2156564419, 742073813491, 784009188701, 3093211012526647, 1240404920534023, 3206211009211419509, 171718219950879367781, 993969333554296364281, 6899316550553351234327, 108706781456610360939660763, 29365306848773629524600829, 376147205196163170923414109869

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Example

a(4) = 1789 because 1789 - 4 = 1785 = 3 * 5 * 7 * 17.

Maple

A191587 := proc(n) for i from 1 do p := ithprime(i) ; if A001221(p-n) = n then return p ; end if; end do: end proc: # R. J. Mathar, Jul 01 2011

Mathematica

Table[k := 2; While[Not[Length[FactorInteger[Prime[k] - n]] == n], k++ ]; Prime[k], {n, 1, 8}]

Prog

(PARI) A191587List(m) = local(j=1, p); for(n=1, m, p=prime(j); while(omega(p-n)!=n, p=prime(j++)); print1(p, ", "));
  default(primelimit, 2200000); A191587List(7); \\ Klaus Brockhaus, Jun 21 2011
(Haskell)
a191587 n = head [p | p <- dropWhile (<= n) a000040_list,
                      a001221 (p - n) == n]
-- Reinhard Zumkeller, Jun 24 2015

Crossrefs

Cf. A097977.

Cf. A000040, A001221.

Sequence in context: A342365 A179596 A339647 * A290411 A142868 A171875

Adjacent sequences: A191584 A191585 A191586 * A191588 A191589 A191590

Keyword

nonn,hard

Author

Michel Lagneau, Jun 07 2011

Extensions

a(10)-a(16) from Donovan Johnson, Jan 14 2012

a(17)-a(20) from Robert Israel, Mar 27 2020

Status

approved