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A217407 Numbers of the form 3^r * 5^s whose decimal representation has a prime number of each digit 0-9. 13
38171039656829610443115234375, 129892841018736362457275390625, 1766298261467341813095601383375, 83480063729486358039093017578125, 715350795894273434303718560266875, 172661884789704345166683197021484375, 65186341275865666700926353804318984375, 5280093643345119002775034658149837734375 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence in particular is motivated by the coincidence that both (2^41)*(3^43) and (3^43)*(5^47) have prime numbers of each digit.
LINKS
FORMULA
a(n) = 3^A217408(n) * 5^A217409(n).
EXAMPLE
The first term here is (3^35)*(5^17), corresponding to A217408(1)=35 and A217409(1)=17. Its decimal representation has two each of 0's, 2's, 7's, 8's and 9's; three each of 4's, 5's and 6's; and 5 each of 1's and 3's.
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(3^r*5^s, r=0..floor(log[3](N/5^s))), s=0..floor(log[5](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(5), t=5^a; while(t<=lim, if(prDigits(t), listput(v, t)); t*=3)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Sep 19 2013
CROSSREFS
Subsequence of A215876.
Sequence in context: A105301 A104300 A095450 * A280350 A095452 A068214
KEYWORD
nonn,base,less
AUTHOR
James G. Merickel, Oct 02 2012
EXTENSIONS
More terms from Robert Israel, May 08 2017
STATUS
approved

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Last modified March 28 08:00 EDT 2024. Contains 371235 sequences. (Running on oeis4.)