Original entry on oeis.org
35, 20, 59, 42, 63, 5, 69, 73, 21, 43, 71, 1149
Offset: 1
The first number that has only 3 and 5 as prime factors and has prime counts of each digit 0-9 in its decimal representation is (3^35)*(5^17), so, corresponding to that being A217407(1), this sequence's first term is 35.
-
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)); apply(k -> valuation(k,3), vecsort(Vec(v))) \\ Charles R Greathouse IV, Sep 19 2013
Original entry on oeis.org
17, 28, 3, 17, 4, 47, 7, 7, 54, 47, 159, 1610
Offset: 1
A217407=(3^35)*(5^17), so this sequence's first term is 17.
-
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)); apply(k -> valuation(k,5), vecsort(Vec(v))) \\ Charles R Greathouse IV, Sep 19 2013
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
A217410
Numbers of the form 3^r*7^s whose decimal representations are such that each digit 0-9 appears a prime number of times.
Original entry on oeis.org
127194058437252046971768387, 13246352657250963177488450589, 1461157813024707015061910842923, 12415617112031938486785960616347, 147856680363717377959300292543841
Offset: 1
A217411(1)=37 and A217412(1)=10, so this sequence's first term is (3^37)*(7^10). It is the smallest number with exactly 3 and 7 as its prime factors to have decimal representation with each digit 0-9 counted a prime number of times. The digits 0, 2, 3, 5, 6 and 9 occur two times each; 1, 4 and 8 occur three times each; and 7 occurs five times.
Cf.
A216854,
A217411,
A217412,
A217404,
A217407,
A217410,
A217416,
A217419,
A217422,
A217425,
A217428,
A217431.
A217422
Numbers of the form 2^r*17^s whose decimal representations are such that each digit 0-9 appears a prime number of times.
Original entry on oeis.org
981750581622330147995648, 28801196957834700781586432, 835992910761480393266512789504, 7295132596707416278470844481536, 76976152675689985407324172386304
Offset: 1
A217423(1)=47 and A217424(1)=8, so this sequence's first term is 2^47 * 17^8. It has in its decimal representation two copies each of the digits 0, 2, 3, 4, 6 and 7; and three copies each of 1, 5, 8 and 9.
Cf.
A217854,
A217423,
A217424,
A217404,
A217407,
A217410,
A217413,
A217416,
A217419,
A217425,
A217428,
A217431.
A217425
Numbers of the form 5^r*7^s whose decimal representations are such that each digit 0-9 appears a prime number of times.
Original entry on oeis.org
97402668820327149658203125, 81209257154451887573232591061530625, 13375863052949754169544537548117223100875, 4587921027161765680153776379004207523600125, 2478309849684200670569842256516437530517578125
Offset: 1
A217426(1)=13 and A217427(1)=20, so this sequence's first term is 5^13 * 7^20. It has two copies each of the digits 1, 3, 4, 5, 7 and 9; three each of 0's, 6's and 8's; and five 2's.
Cf.
A217854,
A217426,
A217427,
A217404,
A217407,
A217410,
A217413,
A217416,
A217419,
A217422,
A217428,
A217431.
A217431
Numbers of the form 3^r*13^s whose decimal representation has a prime number of copies of each digit 0-9.
Original entry on oeis.org
691159348276025798403, 510798409623548623605717, 5097400863986495932124683149477, 10996481542736751381410324522244489, 915432679064411834115450778445909529
Offset: 1
a(1) = 3^25 * 13^8 (so A217432(1)=25 and A217432(1)=8). Indeed, it contains two copies of each digit other than 9 and three copies of 9. No smaller 21-digit number with this general character -- two copies of all but one digit -- and no 20-digit number with two copies of each digit has form 3^a*13^b with a,b > 0.
Cf.
A217854,
A217432,
A217433,
A217404,
A217407,
A217410,
A217413,
A217416,
A217419,
A217422,
A217425,
A217428.
-
nd = 50; mx = 10^nd; pr = Prime@ Range@ PrimePi@ nd; pQ[n_] := Union[DigitCount@n, pr] == pr; Sort@ Select[ Flatten@ Table[3^p*13^q, {p, Log[3, mx/13]}, {q, Log[13, mx/3^p]}], pQ] (* terms < 10^50, Giovanni Resta, Jan 16 2014 *)
A217413
Numbers of the form 2^r*11^s whose decimal representations are such that each digit 0-9 appears a prime number of times.
Original entry on oeis.org
380270922216319615655477248, 804540132953535715766960128, 808356196450619282354367102976, 3705202243778559670466281109192704, 29084192305393678777275954501779456
Offset: 1
A217414(1)=71 and A217415(1)=5, so this sequence's first term is 2^71 * 11^5. It has two each of 0's, 3's, 4's, 6's, 8's and 9's; three each of 1's, 5's and 7's; and five 2's.
Cf.
A217854,
A217414,
A217415,
A217404,
A217407,
A217410,
A217416,
A217419,
A217422,
A217425,
A217428,
A217431.
A217416
Numbers of the form 2^r*13^s whose decimal representations are such that each digit 0-9 appears a prime number of times.
Original entry on oeis.org
19461082905477938625332224, 1493825030770756769826391724130304, 1341437769548771819714842333610521088, 1888426137230419620556768936800026624
Offset: 1
A217417(1)=10 and A217418(1)=20, so this sequence's first term can be simply written as 338^10 (338=2*13^2). It has two each of 0's, 1's, 5's, 6's, 7's and 8's; three each of 3's, 4's and 9's; and five 2's.
Cf.
A217854,
A217417,
A217418,
A217404,
A217407,
A217410,
A217413,
A217419,
A217422,
A217425,
A217428,
A217431.
A217428
Numbers of the form 2^r*19^s whose decimal representation contains each digit 0-9 a prime number of times.
Original entry on oeis.org
611897345462967423035506688, 98653640312161724942079430255181824, 195052744758517664687371356106391552, 69210613747809022824201189555756335104, 401770033097538379880522919696423452672
Offset: 1
2^55 * 19^8 has two copies of each of the digits 0, 1, 2, 7 and 9; three copies of each of 3, 4, 5 and 8; and five copies of the digit 6. All smaller numbers of the required type have at least a digit counted 0, 1, or a composite number of times, so this is a(1).
Cf.
A217854,
A217429,
A217430,
A217404,
A217407,
A217410,
A217413,
A217416,
A217419,
A217422,
A217425,
A217431.
-
nd = 50; mx = 10^nd; pr = Prime@Range@PrimePi@nd; pQ[n_] := Union[DigitCount@n, pr] == pr; Sort@ Select[Flatten@ Table[2^p 19^q, {p, Log[2, mx/19]}, {q, Log[19, mx/2^p]}], pQ] (* Giovanni Resta, Jan 16 2014 *)
Showing 1-10 of 12 results.
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