A217404 Numbers of the form 2^r * 7^s whose decimal representation has a prime number of each digit 0-9.

326249942735257021186048, 3059867626981844171358208, 1745397244661045235955007488, 3297183493952696040281709568, 53076679184360679286299951104, 55415762982862962349014692709376

Offset

1,1

Comments

This sequence's prior, erroneous, title, was 'Numbers with squarefree part 14 whose decimal representations have a prime number of copies of each digit 0-9'. James G. Merickel, Sep 19 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..18

Formula

A217404(n) = 2^A217405(n) * 7^A217406(n).

Example

A217405(1)=36 and A217406(1)=15, giving this sequence's first value as (2^36)*(7^15). Its decimal representation can be seen to have two each of 0's, 1's, 3's, 5's, 6's, 7's, 8's and 9's; and three each of 2's and 3's (prime number counts of each digit).

Maple

N:= 10^100: # to get all terms <= N
filter:= proc(n) local L, P, d;
  L:= convert(n, base, 10);
  P:= Vector(10);
  for d in L do P[d+1]:= P[d+1]+1 od:
  andmap(isprime, P);
end proc:
sort(select(filter, [seq(seq(2^r*7^s, r=0..floor(log[2](N/7^s))), s=0..floor(log[7](N)))])); # Robert Israel, May 08 2017

Prog

(PARI) prDigits(n)=my(d=digits(n), v=vector(10)); for(i=1, #d, v[d[i]+1]++); for(i=1, 10, if(!isprime(v[i]), return(0))); 1
list(lim)=my(v=List(), t); for(a=0, log(lim+.5)\log(7), t=7^a; while(t<=lim, if(prDigits(t), listput(v, t)); t<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Sep 19 2013

Crossrefs

Subsequence of A215876.

Cf. A216854, A217405, A217406, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217428, A217431.

Sequence in context: A008871 A008915 A280346 * A003813 A003806 A257374

Adjacent sequences: A217401 A217402 A217403 * A217405 A217406 A217407

Keyword

nonn,base,less

Author

James G. Merickel, Oct 02 2012

Extensions

Name changed to remove ambiguity by James G. Merickel, Sep 17 2013

Status

approved