cp's OEIS Frontend

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

%I A217404 #39 Apr 06 2020 18:38:04
%S A217404 326249942735257021186048,3059867626981844171358208,
%T A217404 1745397244661045235955007488,3297183493952696040281709568,
%U A217404 53076679184360679286299951104,55415762982862962349014692709376
%N A217404 Numbers of the form 2^r * 7^s whose decimal representation has a prime number of each digit 0-9.
%C A217404 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
%H A217404 Charles R Greathouse IV, <a href="/A217404/b217404.txt">Table of n, a(n) for n = 1..18</a>
%F A217404 A217404(n) = 2^A217405(n) * 7^A217406(n).
%e A217404 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).
%p A217404 N:= 10^100: # to get all terms <= N
%p A217404 filter:= proc(n) local L,P,d;
%p A217404   L:= convert(n,base,10);
%p A217404   P:= Vector(10);
%p A217404   for d in L do P[d+1]:= P[d+1]+1 od:
%p A217404   andmap(isprime,P);
%p A217404 end proc:
%p A217404 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
%o A217404 (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
%o A217404 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
%Y A217404 Subsequence of A215876.
%Y A217404 Cf. A216854, A217405, A217406, A217407, A217410, A217413, A217416, A217419, A217422, A217425, A217428, A217431.
%K A217404 nonn,base,less
%O A217404 1,1
%A A217404 _James G. Merickel_, Oct 02 2012
%E A217404 Name changed to remove ambiguity by _James G. Merickel_, Sep 17 2013