A108382
Primes p such that p's set of distinct digits is {1,3,7}.
Original entry on oeis.org
137, 173, 317, 1373, 1733, 3137, 3371, 7331, 11173, 11317, 11731, 13171, 13177, 13337, 13711, 17137, 17317, 17333, 17377, 17713, 17737, 31177, 31337, 31771, 33317, 33713, 37117, 37171, 37313, 37717, 71317, 71333, 71713, 73133, 73331
Offset: 1
Cf.
A108383 ({1, 3, 9}),
A108384 ({1, 7, 9}),
A108385 ({3, 7, 9}),
A108386 ({1, 3, 7, 9}),
A030096 (Primes whose digits are all odd).
-
S1[1] := {1}: S3[1]:= {3}: S7[1]:= {7}:
S13[1]:= {}: S17[1]:= {}: S37[1]:={}:
S137[1]:= {}:
for n from 2 to 5 do
S1[n]:= map(t -> 10*t+1, S1[n-1]);
S3[n]:= map(t -> 10*t+3, S3[n-1]);
S7[n]:= map(t -> 10*t+7, S7[n-1]);
S13[n]:= map(t -> 10*t+1, S13[n-1] union S3[n-1]) union
map(t -> 10*t+3, S13[n-1] union S1[n-1]);
S17[n]:= map(t -> 10*t+1, S17[n-1] union S7[n-1]) union
map(t -> 10*t+7, S17[n-1] union S1[n-1]);
S37[n]:= map(t -> 10*t+3, S37[n-1] union S7[n-1]) union
map(t -> 10*t+7, S37[n-1] union S3[n-1]);
S137[n]:= map(t -> 10*t+1, S137[n-1] union S37[n-1]) union
map(t -> 10*t+3, S137[n-1] union S17[n-1]) union
map(t -> 10*t+7, S137[n-1] union S13[n-1]);
od:
sort(convert(`union`(seq(select(isprime,S137[n]),n=3..5)),list)); # Robert Israel, Jan 16 2019
-
Select[Prime[Range[7300]],Union[IntegerDigits[#]]=={1,3,7}&] (* Harvey P. Dale, Jun 11 2013 *)
A108383
Primes p such that p's set of distinct digits is {1,3,9}.
Original entry on oeis.org
139, 193, 1193, 1319, 1399, 1913, 1931, 1933, 1993, 3119, 3191, 3319, 3391, 3911, 3919, 3931, 9133, 9311, 9319, 9391, 9931, 11393, 11399, 11933, 11939, 13339, 13399, 13913, 13931, 13933, 13999, 19139, 19319, 19333, 19391, 19913, 19993, 31139
Offset: 1
Cf.
A108382 ({1, 3, 7}),
A108384 ({1, 7, 9}),
A108385 ({3, 7, 9}),
A108386 ({1, 3, 7, 9}),
A030096 (Primes whose digits are all odd).
-
Select[(Table[FromDigits/@Tuples[{1,3,9},n],{n,3,5}]//Flatten),PrimeQ[#] && Min[ DigitCount[#,10,{1,3,9}]]>0&] (* Harvey P. Dale, Apr 09 2017 *)
A108384
Primes p such that p's set of distinct digits is {1,7,9}.
Original entry on oeis.org
179, 197, 719, 971, 1979, 1997, 7919, 9719, 9791, 11197, 11719, 11779, 11971, 17191, 17791, 17911, 17971, 17977, 19717, 19777, 19979, 19997, 71119, 71191, 71719, 71917, 71971, 71999, 77191, 77719, 79111, 91711, 91771, 91997, 97117, 97171
Offset: 1
Cf.
A108382 ({1, 3, 7}),
A108383 ({1, 3, 9}),
A108385 ({3, 7, 9}),
A108386 ({1, 3, 7, 9}),
A030096 (Primes whose digits are all odd).
-
Flatten[Table[Select[FromDigits/@Select[Tuples[{1,7,9},n],Union[#]=={1,7,9}&],PrimeQ],{n,3,5}]] (* Harvey P. Dale, Feb 15 2016 *)
-
lista(nn) = forprime(p=179, nn, if(vecsort(digits(p), , 8)==[1, 7, 9], print1(p, ", "))) \\ Iain Fox, Oct 25 2017
A108385
Primes p such that p's set of distinct digits is {3,7,9}.
Original entry on oeis.org
379, 397, 739, 937, 3739, 3779, 3793, 3797, 7393, 7793, 7933, 7937, 7993, 9337, 9377, 9397, 9733, 9739, 9973, 33739, 33797, 33937, 33997, 37339, 37379, 37397, 37799, 37993, 37997, 39373, 39397, 39733, 39779, 39799, 39937, 39979, 73379, 73939
Offset: 1
Cf.
A108382 ({1, 3, 7}),
A108383 ({1, 3, 9}),
A108384 ({1, 7, 9}),
A108386 ({1, 3, 7, 9}),
A030096 (Primes whose digits are all odd).
-
Table[Select[FromDigits/@Select[Tuples[{3,7,9},n],SubsetQ[#,{3,7,9}]&], PrimeQ],{n,3,5}]//Flatten (* Harvey P. Dale, Sep 15 2016 *)
A108388
Transmutable primes: Primes with distinct digits d_i, i=1,m (2<=m<=4) such that simultaneously exchanging all occurrences of any one pair (d_i,d_j), i<>j results in a prime.
Original entry on oeis.org
13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 179, 191, 199, 313, 331, 337, 773, 911, 919, 1171, 1933, 3391, 7717, 9311, 11113, 11119, 11177, 11717, 11933, 33199, 33331, 77171, 77711, 77713, 79999, 97777, 99991, 113111, 131111, 131113, 131171, 131311
Offset: 1
179 is a term because it is prime and its three transmutations are all prime:
exchanging ('transmuting') 1 and 7: 179 ==> 719 (prime),
exchanging 1 and 9: 179 ==> 971 (prime) and
exchanging 7 and 9: 179 ==> 197 (prime).
(As 791 and 917 are not prime, 179 is not a term of A068652 or A003459 also.).
Similarly, 1317713 is transmutable:
exchanging all 1's and 3s: 1317713 ==> 3137731 (prime),
exchanging all 1's and 7s: 1317713 ==> 7371173 (prime) and
exchanging all 3s and 7s: 1317713 ==> 1713317 (prime).
Cf.
A108382,
A108383,
A108384,
A108385,
A108386,
A108389 (transmutable primes with four distinct digits),
A083983 (transmutable primes with two distinct digits),
A108387 (doubly-transmutable primes),
A006567 (reversible primes),
A002385 (palindromic primes),
A068652 (every cyclic permutation is prime),
A003459 (absolute primes).
-
from gmpy2 import is_prime
from itertools import combinations, count, islice, product
def agen(): # generator of terms
for d in count(2):
for p in product("1379", repeat=d):
p, s = "".join(p), sorted(set(p))
if len(s) == 1: continue
if is_prime(t:=int(p)):
if all(is_prime(int(p.translate({ord(c):ord(d), ord(d):ord(c)}))) for c, d in combinations(s, 2)):
yield t
print(list(islice(agen(), 50))) # Michael S. Branicky, Dec 15 2023
A108389
Transmutable primes with four distinct digits.
Original entry on oeis.org
133999337137, 139779933779, 173139331177, 173399913979, 177793993177, 179993739971, 391331737931, 771319973999, 917377131371, 933971311913, 997331911711, 1191777377177, 9311933973733, 9979333919939, 19979113377173, 31997131171111, 37137197179931, 37337319113911
Offset: 1
a(0)=133999337137 is the smallest transmutable prime with four distinct digits (1,3,7,9):
exchanging all 1's and 3's: 133999337137 ==> 311999117317 (prime),
exchanging all 1's and 7's: 133999337137 ==> 733999331731 (prime),
exchanging all 1's and 9's: 133999337137 ==> 933111337937 (prime),
exchanging all 3's and 7's: 133999337137 ==> 177999773173 (prime),
exchanging all 3's and 9's: 133999337137 ==> 199333997197 (prime) and
exchanging all 7's and 9's: 133999337137 ==> 133777339139 (prime).
No smaller prime with four distinct digits transmutes into six other primes.
Cf.
A108386 (Primes p such that p's set of distinct digits is {1, 3, 7, 9}),
A108388 (transmutable primes),
A083983 (transmutable primes with two distinct digits),
A108387 (doubly-transmutable primes),
A006567 (reversible primes),
A002385 (palindromic primes),
A068652 (every cyclic permutation is prime),
A107845 (transposable-digit primes),
A003459 (absolute primes),
A057876 (droppable-digit primes).
A108418
Primes with at least one of each odd digit and no even digits.
Original entry on oeis.org
13597, 13759, 15739, 15937, 15973, 17359, 17539, 19753, 31957, 37159, 37591, 37951, 39157, 51973, 53197, 53719, 53791, 53917, 57139, 57193, 71359, 71593, 73951, 75193, 75391, 75913, 75931, 79153, 79531, 91573, 91753, 95317, 95713, 95731
Offset: 1
Cf.
A030096 (Primes whose digits are all odd),
A050288 (Pandigital primes),
A108386 (Primes p such that p's set of distinct digits is {1, 3, 7, 9}).
-
Select[Table[Prime[n],{n,10000}],!ContainsAny[IntegerDigits[#],{0,2,4,6,8}]&&ContainsAll[IntegerDigits[#],{1,3,5,7,9}]&] (* James C. McMahon, Mar 05 2024 *)
-
from sympy import isprime
from itertools import count, islice, product
def agen():
for d in count(5):
for p in product("13579", repeat=d):
if set(p) != set("13579"): continue
t = int("".join(p))
if isprime(t): yield t
print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 08 2022
Added missing last term with 5 different digits,
Carmine Suriano, Jan 14 2011
A158917
Emirps using each of the digits 1, 3, 7, 9 at least once, but no others.
Original entry on oeis.org
3719, 3917, 7193, 9173, 17393, 17939, 19793, 19973, 31799, 37199, 37991, 39371, 39791, 71399, 79319, 91397, 93971, 99173, 99317, 99713, 113797, 117193, 119773, 131797, 133379, 137993, 139397, 171937, 177319, 179173, 179939, 191137, 191173, 193337, 193799, 193937, 199337, 199739
Offset: 1
137993, 171937, 179939 etc. inserted by
R. J. Mathar, Apr 04 2009
Showing 1-8 of 8 results.
Comments