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A156343
Primes with equal number of prime and nonprime digits.
3
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
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved