A036313 - OEIS

%I #33 Jul 22 2022 16:42:58

%S 4,8,16,32,58,64,116,128,232,256,458,464,512,841,916,928,1024,1682,

%T 1832,1856,1858,2048,3364,3664,3712,3716,4096,5998,6641,6728,7328,

%U 7424,7432,8192,11996,13282,13456,14656,14848,14864,16384,19858,23992,24389

%N Composite numbers whose prime factors contain no digits other than 2 and 9.

%C All terms are a product of at least two terms of A020460. - _David A. Corneth_, Oct 09 2020

%H David A. Corneth, <a href="/A036313/b036313.txt">Table of n, a(n) for n = 1..10000</a> (first 3266 terms from Robert Israel)

%H <a href="/index/Pri#prime_factors">Index entries for sequences related to prime factors</a>.

%F Sum_{n>=1} 1/a(n) = Product_{p in A020460} (p/(p - 1)) - Sum_{p in A020460} 1/p - 1 = 0.5433646773... . - _Amiram Eldar_, May 18 2022

%p S[1]:= [2,9]:

%p for d from 2 to 5 do S[d]:= map(t -> (10*t+2,10*t+9), S[d-1]) od:

%p P29:= select(isprime, map(op,[seq(S[i],i=1..5)])):

%p N:= 10^5:

%p R:= {1}:

%p for p in P29 do

%p   R:= map(t -> seq(t*p^j,j=0..floor(log[p](N/t))), R)

%p od:

%p R:= R minus convert(P29,set) minus {1}:

%p sort(convert(R,list)); # _Robert Israel_, Jan 17 2020

%t pf29Q[n_]:=Module[{pfs=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},MatchQ[pfs,{2}]||MatchQ[pfs,{9} ]||MatchQ[pfs,{2,9}]]; nn=25000;Select[Complement[Range[nn],Prime[ Range[ PrimePi[nn]]]],pf29Q] (* _Harvey P. Dale_, Apr 23 2012 *)

%Y Cf. A020460, A036302-A036325.

%K nonn,easy,base

%O 1,1

%A _Patrick De Geest_, Dec 15 1998