A081311 - OEIS

A081311

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

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..]