

A217431


Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 09.


13




OFFSET

1,1


COMMENTS

See the formula section for more data, and others in crossreference 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 21digit number with this general character  two copies of all but one digit  and no 20digit 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



