A217405 -id:A217405 - 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.

326249942735257021186048, 3059867626981844171358208, 1745397244661045235955007488, 3297183493952696040281709568, 53076679184360679286299951104, 55415762982862962349014692709376

Offset: 1

James G. Merickel, Oct 02 2012

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

			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).

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

Subsequence of A215876.

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

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

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

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

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

A217406 7-adic valuation of A217404.

Original entry on oeis.org

15, 19, 13, 29, 3, 34, 31, 43, 24, 2, 14, 11, 11, 29, 14, 4, 55, 89

Offset: 1

James G. Merickel, Oct 02 2012

See main sequence, A217404.

			A217404(1)=(2^36)*(7^15), so this sequence's first term is 15, the exponent on 7 in the main sequence.

Subsequence of A215876.

Cf. A217404, A217405.

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)); apply(k -> valuation(k,7), vecsort(Vec(v))) \\ Charles R Greathouse IV, Sep 19 2013

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

Formula

Extensions