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%I #23 Sep 07 2014 08:41:27
%S 691159348276025798403,510798409623548623605717,
%T 5097400863986495932124683149477,10996481542736751381410324522244489,
%U 915432679064411834115450778445909529
%N Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.
%C See the formula section for more data, and others in cross-reference for motivation and similar.
%C a(6), if it exists, is larger than 10^1000. - _Giovanni Resta_, Jan 16 2014
%F A217431(n) = 3^A217432(n) * 13^A217433(n).
%e 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.
%t 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 *)
%Y Cf. A217854, A217432, A217433, A217404, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217428.
%K nonn,base,less
%O 1,1
%A _James G. Merickel_, Oct 05 2012
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