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

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<n, if(isprime(n-k), return(1)); k<<=1)); 0 \\ Charles R Greathouse IV, Sep 01 2015

Crossrefs

A118955 is a subsequence.

Union of A081312 and A081313.

Cf. A000040, A003586.

Sequence in context: A009056 A065475 A062983 * A366935 A053233 A121818

Adjacent sequences: A081308 A081309 A081310 * A081312 A081313 A081314

Keyword

nonn

Author

Reinhard Zumkeller, Mar 17 2003

Status

approved