A087511
Primes consisting only of digits 1 and 3 occurring with equal frequency.
Original entry on oeis.org
13, 31, 11313331, 11333131, 13111333, 13131133, 13131331, 13133311, 13311313, 31133131, 33113131, 1113131333, 1131131333, 1131311333, 1131331133, 1133111333, 1133113133, 1133133311, 1133311313, 1133313113, 1133313131, 1133331113, 1311113333, 1311311333, 1311313313
Offset: 1
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sort(select(isprime,[seq(seq((10^(2*d)-1)/9+2*add(10^i, i=s), s=combinat:-choose([$0..(2*d-1)], d)), d=[1,2,4,5,7,8,10])])); # Robert Israel, Jul 09 2018
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Union[FromDigits/@Select[Flatten[Table[Tuples[{1,3},k],{k,10}],1], PrimeQ[FromDigits[#]] && Count[#,1]==Count[#,3] &]] (* Jayanta Basu, May 19 2013 *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,1,3,isprime))) \\ Andrew Howroyd, Sep 21 2024
A087513
Primes consisting only of digits 1 and 6 occurring with equal frequency.
Original entry on oeis.org
61, 16166611, 16616161, 61116661, 61661161, 66161611, 1166116661, 1166166161, 1166166611, 1166616161, 1616616611, 1661116661, 6111166661, 6111666611, 6116116661, 6161161661, 6161166161, 6161166611, 6161661161, 6166111661, 6166161161, 6611616611, 6616161161, 6616161611
Offset: 1
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Table[Select[FromDigits/@Permutations[PadRight[{},2*n,{1,6}]],PrimeQ],{n,5}]//Flatten//Sort (* Harvey P. Dale, May 28 2019 *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,1,6,isprime))) \\ Andrew Howroyd, Sep 21 2024
A087515
Primes consisting only of digits 1 and 9 occurring with equal frequency.
Original entry on oeis.org
19, 11919199, 11919991, 19111999, 19199119, 19911919, 19991911, 91919911, 91999111, 99111919, 99119191, 99919111, 1111919999, 1111999199, 1191911999, 1191919991, 1191991991, 1191999119, 1199911919, 1199911991, 1199919191, 1199919911, 1911919199, 1911991919
Offset: 1
A087512
Primes consisting only of digits 1 and 4 occurring with equal frequency.
Original entry on oeis.org
41, 14441411, 41414411, 44114141, 1144141441, 1144144411, 1144441141, 1411414441, 1441411441, 1441444111, 1444114141, 4111144441, 4111444411, 4114414141, 4141141441, 4141144141, 4144111441, 4411114441, 4411144141, 4411414411, 4414141141, 4414441111
Offset: 1
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Union[Flatten[Table[Select[FromDigits/@Permutations[Flatten[Table[{1,4},{n}]]],PrimeQ],{n,5}]]] (* Harvey P. Dale, Nov 21 2014 *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,1,4,isprime))) \\ Andrew Howroyd, Sep 21 2024
A087514
Primes consisting only of digits 1 and 7 occurring with equal frequency.
Original entry on oeis.org
17, 71, 11171777, 11177717, 17111777, 17171177, 17171771, 17177117, 17711717, 17717171, 71117177, 71171717, 71717117, 77111717, 77711171, 1111717777, 1117117777, 1117177177, 1117771177, 1117771717, 1177117177, 1177177711, 1177711177, 1177717171, 1177717711
Offset: 1
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Sort[Select[FromDigits/@Flatten[Table[Permutations[PadRight[{},2n,{1,7}]],{n,5}],1],PrimeQ]] (* Harvey P. Dale, Jul 27 2019 *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,1,7,isprime))) \\ Andrew Howroyd, Sep 21 2024
A087527
Primes consisting only of digits 2 and 3 occurring with equal frequency.
Original entry on oeis.org
23, 23223323, 32323223, 2222323333, 2223223333, 2232223333, 2232322333, 2232332233, 2323222333, 2332322233, 2333222323, 2333223223, 3223232323, 3232222333, 3232232233, 3232233223, 3232322323, 3323232223, 22222232333333, 22222322333333, 22222323233333
Offset: 1
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,2,3,isprime))) \\ Andrew Howroyd, Sep 21 2024
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from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits):
alst = []
for d in range(2, maxdigits + 1, 2):
ms = "2"*(d//2) + "3"*(d//2 - 1)
for p in multiset_permutations(ms, d-1):
t = int("".join(p) + "3")
if isprime(t):
alst.append(t)
return alst
print(auptodigs(10)) # Michael S. Branicky, Jan 11 2022
Offset changed to 1 and a(19) corrected by
Georg Fischer, Jan 11 2022
A087528
Primes consisting only of digits 2 and 9 occurring with equal frequency.
Original entry on oeis.org
29, 22929299, 29229929, 29299229, 29992229, 92922299, 99292229, 2229922999, 2229929929, 2229992299, 2292229999, 2292929299, 2292999229, 2299222999, 2299292929, 2299922929, 2922929929, 2922992299, 2929292299, 2929299229, 2992299229, 2992922299, 2992992229, 2999229229
Offset: 1
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F:= proc(d) local C,c;
if d mod 3 = 0 then return NULL fi;
C:= map(t -> [0,op(t)], combinat:-choose([$1..d-1],d/2-1));
C:= map(t -> 2*(10^d-1)/9 + 7*add(10^c,c=t), C);
op(sort(select(isprime,C)))
end proc:
seq(F(d),d=2..14,2); # Robert Israel, Oct 30 2019
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,2,9,isprime))) \\ Andrew Howroyd, Sep 21 2024
A087529
Primes consisting only of digits 3 and 4 occurring with equal frequency.
Original entry on oeis.org
43, 34434343, 44334343, 44343433, 3334344443, 3343443443, 3344334443, 3344344343, 3344434433, 3433434443, 3433444433, 3434444333, 3443343443, 3444334343, 4334433443, 4334443433, 4343444333, 4344333443, 4344433343, 4344443333, 4433343443, 4433344343, 4434334343
Offset: 1
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Select[FromDigits/@Flatten[Permutations/@Table[PadRight[{},2n,{4,3}],{n,5}],1],PrimeQ]//Sort (* Harvey P. Dale, Aug 08 2017 *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,3,4,isprime))) \\ Andrew Howroyd, Sep 21 2024
A087530
Primes consisting only of digits 3 and 5 occurring with equal frequency.
Original entry on oeis.org
53, 35553533, 53355353, 53533553, 3335553553, 3355335553, 3355355533, 3355533553, 3355535353, 3535355353, 3553535353, 3553555333, 3555353353, 3555353533, 3555533533, 5353353553, 5353533553, 5353553533, 5355353533, 5355533353, 5533553353, 5535535333
Offset: 1
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Sort[Select[FromDigits/@Flatten[Permutations/@Table[PadRight[{},2n,{3,5}],{n,5}],1],PrimeQ]] (* Harvey P. Dale, Oct 24 2012 *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,3,5,isprime))) \\ Andrew Howroyd, Sep 20 2024
A087531
Primes consisting only of digits 3 and 7 occurring with equal frequency.
Original entry on oeis.org
37, 73, 33373777, 33773737, 37373773, 37377337, 73337377, 73337773, 73373737, 73773373, 77337373, 77733373, 3337737737, 3337777337, 3377733773, 3733377377, 3733733777, 3737733773, 3773333777, 3773337377, 3773733737, 3777333773, 3777337337, 3777337373
Offset: 1
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Select[Flatten[Table[FromDigits/@Permutations[Join[Table[3, {i}], Table[7, {i}]]], {i, 7}]], PrimeQ] (* from Harvey P. Dale *)
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\\ Needs B() from A087510.
concat(vector(6,k,B(k,3,7,isprime))) \\ Andrew Howroyd, Sep 20 2024
Showing 1-10 of 19 results.
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