A082646 Primes whose decimal expansions contain equal numbers of each of their digits.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 317, 347, 349, 359, 367, 379, 389, 397, 401

Offset: 1

Author

Rick L. Shepherd, May 24 2003

Keywords

• base
• nonn

Comments

All repunit primes (A004022) are terms. There are no terms of prime p digit- length for p >= 11 unless p is a term of A004023 - in which case there is exactly one such term here, the repunit prime of length p. The smallest term whose digits are neither all the same nor all different is 100313. No term of digit-length 10 can have digits all different because such a term would be divisible by 3 (as 45, the sum of its digits, would be divisible by 3).

Examples

			The prime 101 is not a term because it contains two 1's but only one 0.
The prime 127 is a term because it has one 1, one 2 and one 7.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004022 (repunit primes), A004023 (digit lengths of repunit primes).

Programs

Mathematica

t={}; Do[p=Prime[n]; If[Length[DeleteDuplicates[Transpose[Tally[IntegerDigits[p]]][[2]]]]==1,AppendTo[t,p]],{n,79}]; t (* Jayanta Basu, May 10 2013 *)

Python

from sympy import prime
A082646_list = []
for i in range(1,10**5):
    p = str(prime(i))
    h = [p.count(d) for d in '0123456789' if d in p]
    if min(h) == max(h):
        A082646_list.append(int(p)) # Chai Wah Wu, Mar 06 2016