A217431 Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.

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

Links

Table of n, a(n) for n=1..5.

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 *)

Crossrefs

Cf. A217854, A217432, A217433, A217404, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217428.

Sequence in context: A338967 A239924 A181791 * A173471 A291215 A115541

Adjacent sequences: A217428 A217429 A217430 * A217432 A217433 A217434

Keyword

nonn,base,less

Author

James G. Merickel, Oct 05 2012

Status

approved