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%I #16 Nov 12 2019 15:05:17
%S 38294359833110460235776,17428188652935605013970944,
%T 20655630996071828164706304,2414716733802996890553286656,
%U 3721583168194563820184970816,4829433467605993781106573312,10455147226971833612810452992,27880392605258222967494541312,30526789326102084147241549824
%N 3-smooth numbers (i.e., of the form 2^a*3^b) such that each digit 0-9 occurs a prime number of times.
%C Obviously such numbers need to have at least 10 x 2 = 20 digits, but the smallest solution a(1)=2^56*3^12 has actually 5 digits "3", and 2 of each of the other digits.
%H Charles R Greathouse IV, <a href="/A216854/b216854.txt">Table of n, a(n) for n = 1..40</a>
%H J. Merickel, <a href="http://groups.yahoo.com/group/primenumbers/message/24454">Conjecture</a>, Sept. 2012
%H James Merickel and others, <a href="/A216854/a216854.txt">Conjecture</a>, digest of 30 messages in primenumbers Yahoo group, Sep 16, 2012 - Jul 7, 2014.
%F A216854(n) = 2^A216855(n) * 3^A216856(n).
%o (PARI) is_A216854(n)=my(t=divrem(n,10),c=vector(10)); until(!t=divrem(t[1],10), c[t[2]+1]++); vecmin(isprime(c)) && return(c)
%o (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 list(lim)=my(v=List(), t); for(a=0, log(lim+.5)\log(3), t=3^a; while(t<=lim, if(prDigits(t), listput(v, t)); t<<=1)); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Sep 19 2013
%Y Subsequence of A215876.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Sep 17 2012
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