cp's OEIS Frontend

A036313 Composite numbers whose prime factors contain no digits other than 2 and 9.

%I A036313 #33 Jul 22 2022 16:42:58
%S A036313 4,8,16,32,58,64,116,128,232,256,458,464,512,841,916,928,1024,1682,
%T A036313 1832,1856,1858,2048,3364,3664,3712,3716,4096,5998,6641,6728,7328,
%U A036313 7424,7432,8192,11996,13282,13456,14656,14848,14864,16384,19858,23992,24389
%N A036313 Composite numbers whose prime factors contain no digits other than 2 and 9.
%C A036313 All terms are a product of at least two terms of A020460. - _David A. Corneth_, Oct 09 2020
%H A036313 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 A036313 <a href="/index/Pri#prime_factors">Index entries for sequences related to prime factors</a>.
%F A036313 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 A036313 S[1]:= [2,9]:
%p A036313 for d from 2 to 5 do S[d]:= map(t -> (10*t+2,10*t+9), S[d-1]) od:
%p A036313 P29:= select(isprime, map(op,[seq(S[i],i=1..5)])):
%p A036313 N:= 10^5:
%p A036313 R:= {1}:
%p A036313 for p in P29 do
%p A036313   R:= map(t -> seq(t*p^j,j=0..floor(log[p](N/t))), R)
%p A036313 od:
%p A036313 R:= R minus convert(P29,set) minus {1}:
%p A036313 sort(convert(R,list)); # _Robert Israel_, Jan 17 2020
%t A036313 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 A036313 Cf. A020460, A036302-A036325.
%K A036313 nonn,easy,base
%O A036313 1,1
%A A036313 _Patrick De Geest_, Dec 15 1998