A217404
Numbers of the form 2^r * 7^s whose decimal representation has a prime number of each digit 0-9.
Original entry on oeis.org
326249942735257021186048, 3059867626981844171358208, 1745397244661045235955007488, 3297183493952696040281709568, 53076679184360679286299951104, 55415762982862962349014692709376
Offset: 1
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).
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
A217407
Numbers of the form 3^r * 5^s whose decimal representation has a prime number of each digit 0-9.
Original entry on oeis.org
38171039656829610443115234375, 129892841018736362457275390625, 1766298261467341813095601383375, 83480063729486358039093017578125, 715350795894273434303718560266875, 172661884789704345166683197021484375, 65186341275865666700926353804318984375, 5280093643345119002775034658149837734375
Offset: 1
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.
Cf.
A216854,
A217408,
A217409,
A217404,
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(3^r*5^s, r=0..floor(log[3](N/5^s))),s=0..floor(log[5](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(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
A216854
3-smooth numbers (i.e., of the form 2^a*3^b) such that each digit 0-9 occurs a prime number of times.
Original entry on oeis.org
38294359833110460235776, 17428188652935605013970944, 20655630996071828164706304, 2414716733802996890553286656, 3721583168194563820184970816, 4829433467605993781106573312, 10455147226971833612810452992, 27880392605258222967494541312, 30526789326102084147241549824
Offset: 1
-
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)
-
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(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
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
A217404(1)=(2^36)*(7^15), so this sequence's first term is 15, the exponent on 7 in the main sequence.
-
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
Showing 1-4 of 4 results.
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