A358685 Number of primes < 10^n whose digits are all odd.

3, 15, 57, 182, 790, 3217, 13298, 56866, 254689, 1128121, 5106701, 23266331, 107019385, 494689488, 2306491761, 10758057302, 50548874979

Offset: 1

Author

Zhining Yang, Nov 26 2022

Keywords

• base
• nonn
• more

Examples

			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.
		

Links

• BBS Math Blog, How many prime numbers are all composed of 1,3,5,7,9? (in Chinese).

Crossrefs

Cf. A030096, A358690.

Programs

Mathematica

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 *)

Python

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)])

Python

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

Extensions

a(10)-a(14) from Michael S. Branicky, Nov 26 2022

a(15) from Zhining Yang, Dec 21 2022

a(16)-a(17) from Martin Ehrenstein, Dec 21 2022