A358690 Number of n-digit primes whose digits are all odd.

3, 12, 42, 125, 608, 2427, 10081, 43568, 197823, 873432, 3978580, 18159630, 83753054, 387670103, 1811802273, 8451565541, 39790817677

Offset

1,1

Links

Table of n, a(n) for n=1..17.

Formula

a(n) = A358685(n) - A358685(n-1).

Example

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.

Mathematica

Length[Select[Prime[Range[PrimePi[10^(n - 1)], PrimePi[10^n]]], And @@ OddQ[IntegerDigits[#]] &]]

Prog

(Python)
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)])
(Python)
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

Crossrefs

Cf. A030096, A358685.

Sequence in context: A260153 A328299 A135264 * A084529 A017941 A066972

Adjacent sequences: A358687 A358688 A358689 * A358691 A358692 A358693

Keyword

base,nonn,more

Author

Zhining Yang, Nov 26 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 24 2022

Status

approved