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A081311 Numbers that can be written as sum of a prime and an 3-smooth number.

%I A081311 #26 Oct 13 2021 03:40:18
%S A081311 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,
%T A081311 28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A081311 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
%N A081311 Numbers that can be written as sum of a prime and an 3-smooth number.
%C A081311 A081308(a(n))>0; complement of A081310.
%C A081311 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
%H A081311 Charles R Greathouse IV, <a href="/A081311/b081311.txt">Table of n, a(n) for n = 1..10000</a>
%H A081311 J. Pintz, <a href="https://doi.org/10.1007/s10474-006-0060-6">A note on Romanov's constant</a>, Acta Mathematica Hungarica 112:1-2 (2006), pp. 1-14.
%t A081311 nmax = 1000;
%t A081311 S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
%t A081311 A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
%t A081311 Select[Range[nmax], A081308[#] > 0 &] (* _Jean-François Alcover_, Oct 13 2021 *)
%o A081311 (Haskell)
%o A081311 a081310 n = a081310_list !! (n-1)
%o A081311 a081310_list = filter ((== 0) . a081308) [1..]
%o A081311 -- _Reinhard Zumkeller_, Jul 04 2012
%o A081311 (PARI) is(n)=for(i=0, logint(n,3), my(k=3^i); while(k<n, if(isprime(n-k), return(1)); k<<=1)); 0 \\ _Charles R Greathouse IV_, Sep 01 2015
%Y A081311 A118955 is a subsequence.
%Y A081311 Union of A081312 and A081313.
%Y A081311 Cf. A000040, A003586.
%K A081311 nonn
%O A081311 1,1
%A A081311 _Reinhard Zumkeller_, Mar 17 2003