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

1,1

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).

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A030291 A242541 A052085 * A231588 A038618 A030475

Adjacent sequences: A082643 A082644 A082645 * A082647 A082648 A082649

Keyword

base,nonn

Author

Rick L. Shepherd, May 24 2003

Status

approved