cp's OEIS Frontend

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

%I A082646 #17 May 07 2025 02:22:05
%S A082646 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T A082646 97,103,107,109,127,137,139,149,157,163,167,173,179,193,197,239,241,
%U A082646 251,257,263,269,271,281,283,293,307,317,347,349,359,367,379,389,397,401
%N A082646 Primes whose decimal expansions contain equal numbers of each of their digits.
%C A082646 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).
%H A082646 Chai Wah Wu, <a href="/A082646/b082646.txt">Table of n, a(n) for n = 1..10000</a>
%e A082646 The prime 101 is not a term because it contains two 1's but only one 0.
%e A082646 The prime 127 is a term because it has one 1, one 2 and one 7.
%t A082646 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 *)
%o A082646 (Python)
%o A082646 from sympy import prime
%o A082646 A082646_list = []
%o A082646 for i in range(1,10**5):
%o A082646     p = str(prime(i))
%o A082646     h = [p.count(d) for d in '0123456789' if d in p]
%o A082646     if min(h) == max(h):
%o A082646         A082646_list.append(int(p)) # _Chai Wah Wu_, Mar 06 2016
%Y A082646 Cf. A004022 (repunit primes), A004023 (digit lengths of repunit primes).
%K A082646 base,nonn
%O A082646 1,1
%A A082646 _Rick L. Shepherd_, May 24 2003