A087395 Primes in which the frequency of every digit is the same and is at least 2.

11, 100313, 107071, 110909, 114343, 115757, 116969, 117373, 117979, 118787, 119797, 121727, 127217, 127271, 131939, 133717, 133919, 134341, 136163, 136361, 137713, 140401, 141499, 142421, 143413, 145451, 149419, 149491, 155717, 157571

Offset: 1

Author

Amarnath Murthy, Sep 10 2003

Keywords

• base
• nonn

Comments

If d is prime, the only terms with d digits are repunit primes (A004022). - Robert Israel, Nov 18 2022

Examples

			100313 is a term in which each of the digits 1, 3 and 0 occurs with frequency 2.
		

Links

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

Crossrefs

Contains A004022.

Programs

Maple

filter:= proc(n) local L,d,S;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  S:={seq(numboccur(d,L),d=convert(L,set))};
  nops(S) = 1 and S[1]>=2
end proc:
select(filter, [seq(i,i=11 .. 200000, 2)]); # Robert Israel, Nov 18 2022

Mathematica

fpQ[n_]:=Module[{dc=Union[Cases[DigitCount[n],Except[0]]]}, First[dc]>1 &&Length[dc]==1]; Select[Prime[Range[14500]],fpQ] (* Harvey P. Dale, Apr 22 2011 *)

Python

# see linked program for a faster version
from sympy import isprime
from collections import Counter
from itertools import count, islice
def ok(n):
    cv = Counter(str(n)).values()
    return min(cv) >= 2 and len(set(cv)) == 1 and isprime(n)
def agen():
    evdigs = (k for d in count(2, 2) for k in range(10**(d-1)+1, 10**d, 2))
    yield from (k for k in evdigs if ok(k))
print(list(islice(agen(), 30))) # Michael S. Branicky, Nov 18 2022

Extensions

Corrected and extended by David Wasserman, May 31 2005