This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
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
23 is a member because if the digit 2 is removed the resulting number becomes 3 which is a prime.
Select[Prime@ Range@ 100, PrimeQ[ FromDigits[ Select[ IntegerDigits@#, OddQ]]] &]
isok(p) = isprime(p) && isprime(fromdigits(select(x->(x % 2), digits(p)))); \\ Michel Marcus, Jun 21 2018
2 is in the sequence because 2*(2) - 2 = 2 (prime); 359 is in the sequence because 359*(3*5*9) - 2 = 48463 (prime).
ppd2Q[n_]:=Module[{c=n Times@@IntegerDigits[n]-2},c>0&&PrimeQ[c]]; Select[ Prime[Range[1500]],ppd2Q] (* Harvey P. Dale, Jan 02 2020 *)
P = Primes(); [ P.unrank(p) for p in range(1000) if is_prime( P.unrank(p) * prod([int(i) for i in str(P.unrank(p)) ] ) - 2 )]
Select[Table[FromDigits[PadRight[{},n,{9,7,5,3,1}]],{n,30}],PrimeQ] (* Harvey P. Dale, Jul 13 2021 *)
for(n=2,1e3, if(isprime(t=10^n*97531\99999), print1(t", "))) \\ Charles R Greathouse IV, Dec 09 2024
a(2) = 15 as there are 15 primes less than 100 whose digits are all odd: 3, 5, 7, 11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97.
n=7 Length[Select[Prime[Range[PrimePi[10^n]]], And @@ OddQ[IntegerDigits[#]] &]] (* Zhining Yang, Nov 26 2022 *) n = PrimePi[10^8]; Sum[If[MemberQ[IntegerDigits[Prime[i]], _?EvenQ], 0, 1], {i, 1, n}] (* Jianlin Su, Nov 27 2022 *)
from sympy import primerange
def a(n):
p=list(primerange(3,10**n))
return(sum(1 for k in p if all(int(d) %2 for d in str(k))==True))
print ([a(n) for n in range(1,8)])
from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
c = 3
for d in count(2):
yield c
for p in product("13579", repeat=d-1):
s = "".join(p)
for last in "1379":
if isprime(int(s+last)): c += 1
print(list(islice(agen(), 9))) # Michael S. Branicky, Nov 27 2022
a(2) = 12 as there are 12 2-digit primes whose digits are all odd: 11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97.
Length[Select[Prime[Range[PrimePi[10^(n - 1)], PrimePi[10^n]]], And @@ OddQ[IntegerDigits[#]] &]]
from sympy import primerange
def a(n):
num=0
for f in range(1,10,2):
p=list(primerange(f*10**(n-1),(f+1)*10**(n-1)))
num+=sum(1 for k in p if all(int(d) %2 for d in str(k)))
return(num)
print ([a(n) for n in range(1,8)])
from sympy import isprime
from itertools import count, islice, product
def a(n):
c = 0 if n > 1 else 1
for p in product("13579", repeat=n-1):
s = "".join(p)
for last in "1379":
if isprime(int(s+last)): c += 1
return c
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Nov 27 2022
a(4)=13 is a member because the 9's complements of the digits 1,3 are 8,2, and none of the integers 28 or 82 is prime. a(26)=149 is a member because the 9's complements of its digits are 8,5,0, and none of the integers with those digits is prime.
R:= 3,5: for d from 2 to 4 do P:= select(isprime,[seq(i,i=10^(d-1)+1..10^d-1,2)]); nP:= nops(P); Pd:= map(sort@convert,P,base,10); Ps:= convert(map(t -> ListTools:-Reverse([9$d]-t), Pd),set); S:= remove(t -> member(Pd[t],Ps),[$1..nP]); R:= R, op(P[S]); od: R; # Robert Israel, Oct 06 2020
The 22nd prime is 79, the digits 7 and 9 are odd. Thus 22 is in the sequence. The 9th prime is 23, the digit 2 is even, therefore 9 is not in the sequence.
a={};For[n=1,n<200,n++,If[Length[Select[IntegerDigits[Prime[n]],EvenQ[ # ]&]] == 0, AppendTo[a, n]]]; a
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