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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Cf. A065333.

Sequence in context: A236531 A332334 A217403 * A329377 A010553 A262095

Adjacent sequences: A081306 A081307 A081308 * A081310 A081311 A081312

Keyword

nonn,look

Author

Reinhard Zumkeller, Mar 17 2003

Status

approved