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

1,1

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]

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A154385, A154386, A371352.

Sequence in context: A179909 A220488 A092626 * A154762 A079348 A349667

Adjacent sequences: A156340 A156341 A156342 * A156344 A156345 A156346

Keyword

nonn,base

Author

Juri-Stepan Gerasimov, Feb 08 2009

Status

approved