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

4, 8, 16, 32, 58, 64, 116, 128, 232, 256, 458, 464, 512, 841, 916, 928, 1024, 1682, 1832, 1856, 1858, 2048, 3364, 3664, 3712, 3716, 4096, 5998, 6641, 6728, 7328, 7424, 7432, 8192, 11996, 13282, 13456, 14656, 14848, 14864, 16384, 19858, 23992, 24389

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• easy
• base

Comments

All terms are a product of at least two terms of A020460. - David A. Corneth, Oct 09 2020

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3266 terms from Robert Israel)
• Index entries for sequences related to prime factors.

Crossrefs

Cf. A020460, A036302-A036325.

Programs

Maple

S[1]:= [2,9]:
for d from 2 to 5 do S[d]:= map(t -> (10*t+2,10*t+9), S[d-1]) od:
P29:= select(isprime, map(op,[seq(S[i],i=1..5)])):
N:= 10^5:
R:= {1}:
for p in P29 do
  R:= map(t -> seq(t*p^j,j=0..floor(log[p](N/t))), R)
od:
R:= R minus convert(P29,set) minus {1}:
sort(convert(R,list)); # Robert Israel, Jan 17 2020

Mathematica

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 *)

Formula

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