A156343 Primes with equal number of prime and nonprime digits.

13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 1033, 1123, 1153, 1213, 1217, 1229, 1231, 1259, 1279, 1283, 1297, 1303, 1307, 1321, 1367, 1423, 1427, 1433, 1453, 1531, 1543, 1559, 1567, 1571, 1579, 1583, 1597, 1627, 1637, 1657, 1721, 1747, 1759, 1783, 1787

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 08 2009

Keywords

• nonn
• base

Comments

Prime digits are 2, 3, 5 or 7. Nonprime digits are 0, 1, 4, 6, 8 or 9.

Complement of (A154385 U A154386). [Juri-Stepan Gerasimov, Nov 29 2009]

Examples

			13 (1=nonprime, 3=prime) = a(1).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A154385, A154386, A371352.

Programs

Maple

A109066c := proc(n) nops(convert(n,base,10))-A109066(n) ; end:
A109066 := proc(n) local dgs,a ; dgs := convert(n,base,10) ; a := 0 ; for i in dgs do if isprime(i) then a := a+1 ; fi; od: a ; end:
for i from 1 to 400 do p := ithprime(i) ; if A109066(p) = A109066c(p) then printf("%d,",p) ; fi; od: # R. J. Mathar, Feb 09 2009

Mathematica

Select[Prime[Range[5,300]],Length[Select[IntegerDigits[#],PrimeQ]]==Length[ Select[ IntegerDigits[ #],!PrimeQ[ #]&]]&] (* Harvey P. Dale, Dec 15 2022 *)

Python

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s, counts = str(n), [0, 0]
    for c in s: counts[int(c in "2357")] += 1
    return counts[0] == counts[1]
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Apr 23 2024