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

1,1

Comments

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

Links

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

Michael S. Branicky, Python program

Example

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

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 *)

Prog

(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

Crossrefs

Contains A004022.

Sequence in context: A348644 A165934 A110780 * A199169 A145571 A049193

Adjacent sequences: A087392 A087393 A087394 * A087396 A087397 A087398

Keyword

base,nonn

Author

Amarnath Murthy, Sep 10 2003

Extensions

Corrected and extended by David Wasserman, May 31 2005

Status

approved