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

1,1

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.

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

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 *)

Crossrefs

Cf. A020460, A036302-A036325.

Sequence in context: A189925 A007096 A298356 * A121986 A285906 A172042

Adjacent sequences: A036310 A036311 A036312 * A036314 A036315 A036316

Keyword

nonn,easy,base

Author

Patrick De Geest, Dec 15 1998

Status

approved