

A081311


Numbers that can be written as sum of a prime and an 3smooth 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
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OFFSET

1,1


COMMENTS

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



MATHEMATICA

nmax = 1000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n  s]];


PROG

(Haskell)
a081310 n = a081310_list !! (n1)
a081310_list = filter ((== 0) . a081308) [1..]
(PARI) is(n)=for(i=0, logint(n, 3), my(k=3^i); while(k<n, if(isprime(nk), return(1)); k<<=1)); 0 \\ Charles R Greathouse IV, Sep 01 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



