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

%I A358690 #34 Jan 14 2023 08:44:48
%S A358690 3,12,42,125,608,2427,10081,43568,197823,873432,3978580,18159630,
%T A358690 83753054,387670103,1811802273,8451565541,39790817677
%N A358690 Number of n-digit primes whose digits are all odd.
%F A358690 a(n) = A358685(n) - A358685(n-1).
%e A358690 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.
%t A358690 Length[Select[Prime[Range[PrimePi[10^(n - 1)], PrimePi[10^n]]], And @@ OddQ[IntegerDigits[#]] &]]
%o A358690 (Python)
%o A358690 from sympy import primerange
%o A358690 def a(n):
%o A358690     num=0
%o A358690     for f in range(1,10,2):
%o A358690         p=list(primerange(f*10**(n-1),(f+1)*10**(n-1)))
%o A358690         num+=sum(1 for k in p if all(int(d) %2 for d in str(k)))
%o A358690     return(num)
%o A358690 print ([a(n) for n in range(1,8)])
%o A358690 (Python)
%o A358690 from sympy import isprime
%o A358690 from itertools import count, islice, product
%o A358690 def a(n):
%o A358690     c = 0 if n > 1 else 1
%o A358690     for p in product("13579", repeat=n-1):
%o A358690         s = "".join(p)
%o A358690         for last in "1379":
%o A358690             if isprime(int(s+last)): c += 1
%o A358690     return c
%o A358690 print([a(n) for n in range(1, 10)]) # _Michael S. Branicky_, Nov 27 2022
%Y A358690 Cf. A030096, A358685.
%K A358690 base,nonn,more
%O A358690 1,1
%A A358690 _Zhining Yang_, Nov 26 2022
%E A358690 a(10)-a(14) from _Michael S. Branicky_, Nov 26 2022
%E A358690 a(15) from _Zhining Yang_, Dec 21 2022
%E A358690 a(16)-a(17) from _Martin Ehrenstein_, Dec 24 2022