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A081309
Smallest prime p such that n-p is a 3-smooth number, a(n)=0 if no such prime exists.
2
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
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
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Mar 17 2003
STATUS
approved