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 A081311 Numbers that can be written as sum of a prime and an 3-smooth number. 7
 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A081308(a(n))>0; complement of A081310. Up to 10^n this sequence has 8, 95, 916, 8871, 86974, 858055, 8494293, 84319349, 838308086, ... terms. The lower density is of this sequence is greater than 0.59368 (see Pintz), but seems to be less than 1; can this be proved? Charles R Greathouse IV, Sep 01 2015 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 J. Pintz, A note on Romanov's constant, Acta Mathematica Hungarica 112:1-2 (2006), pp. 1-14. MATHEMATICA nmax = 1000; S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &]; A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]]; Select[Range[nmax], A081308[#] > 0 &] (* Jean-François Alcover, Oct 13 2021 *) PROG (Haskell) a081310 n = a081310_list !! (n-1) a081310_list = filter ((== 0) . a081308) [1..] -- Reinhard Zumkeller, Jul 04 2012 (PARI) is(n)=for(i=0, logint(n, 3), my(k=3^i); while(k

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Last modified December 8 14:30 EST 2023. Contains 367679 sequences. (Running on oeis4.)