A081309 Smallest prime p such that n-p is a 3-smooth number, a(n)=0 if no such prime exists.

0, 0, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 5, 2, 3, 7, 5, 2, 3, 2, 3, 13, 5, 23, 7, 2, 3, 19, 2, 3, 7, 5, 17, 2, 3, 0, 5, 2, 3, 13, 5, 41, 7, 17, 13, 19, 11, 47, 13, 2, 3, 43, 5, 53, 7, 2, 3, 31, 5, 59, 7, 53, 31, 37, 11, 2, 3, 41, 5, 43, 7, 71, 19, 2, 3, 67, 5, 0, 7, 53, 17, 73, 2, 3, 13, 5, 23, 7, 17, 89

Offset: 1

Author

Reinhard Zumkeller, Mar 17 2003

Keywords

• nonn
• look

Examples

			a(25)=7: 25=7+2*3^2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A081310, A081311, A081308, A000040, A003586.

Cf. A065333.

Programs

Haskell

a081309 n | null ps   = 0
          | otherwise = head ps
          where ps = [p | p <- takeWhile (< n) a000040_list,
                          a065333 (n - p) == 1]
-- Reinhard Zumkeller, Jul 04 2012

Mathematica

smooth3Q[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1;
a[n_] := Module[{p}, For[p = 2, p < n, p = NextPrime[p], If[smooth3Q[n - p], Return[p]]]; 0];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 14 2021 *)

Formula

a(n)=0 iff A081308(n)=0.