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A217431
Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.
13
691159348276025798403, 510798409623548623605717, 5097400863986495932124683149477, 10996481542736751381410324522244489, 915432679064411834115450778445909529
OFFSET
1,1
COMMENTS
See the formula section for more data, and others in cross-reference for motivation and similar.
a(6), if it exists, is larger than 10^1000. - Giovanni Resta, Jan 16 2014
FORMULA
A217431(n) = 3^A217432(n) * 13^A217433(n).
EXAMPLE
a(1) = 3^25 * 13^8 (so A217432(1)=25 and A217432(1)=8). Indeed, it contains two copies of each digit other than 9 and three copies of 9. No smaller 21-digit number with this general character -- two copies of all but one digit -- and no 20-digit number with two copies of each digit has form 3^a*13^b with a,b > 0.
MATHEMATICA
nd = 50; mx = 10^nd; pr = Prime@ Range@ PrimePi@ nd; pQ[n_] := Union[DigitCount@n, pr] == pr; Sort@ Select[ Flatten@ Table[3^p*13^q, {p, Log[3, mx/13]}, {q, Log[13, mx/3^p]}], pQ] (* terms < 10^50, Giovanni Resta, Jan 16 2014 *)
KEYWORD
nonn,base,less
AUTHOR
James G. Merickel, Oct 05 2012
STATUS
approved