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A036313
Composite numbers whose prime factors contain no digits other than 2 and 9.
2
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)
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
KEYWORD
nonn,easy,base
AUTHOR
Patrick De Geest, Dec 15 1998
STATUS
approved