A220627 Prime numbers that are not Brazilian.

2, 3, 5, 11, 17, 19, 23, 29, 37, 41, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317

Offset: 1

Author

Bernard Schott, Dec 17 2012

Keywords

• nonn
• base

Comments

These are primes not in A085104 (Brazilian primes).

Primes that are not repunit in any base b >= 2 with three or more digits.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Crossrefs

Cf. A085104.

Programs

Mathematica

brazBases[n_] := Select[Range[2, n - 2], Length[Union[IntegerDigits[n, #]]] == 1 &]; Select[Range[2, 1000], PrimeQ[#] && brazBases[#] == {} &] (* T. D. Noe, Dec 26 2012 *)

PARI

isok(p) = {if (isprime(p), for (b=2, p-1, my(d=digits(p, b), md=vecmin(d)); if ((#d > 2) && (md == 1) && (vecmax(d) == 1), return (0));); return (1););} \\ Michel Marcus, Apr 30 2021

Python

from sympy.ntheory.factor_ import digits
from sympy import isprime, primerange
def B(n):
    l=[]
    for b in range(2, n - 1):
        d=digits(n, b)[1:]
        if max(d)==min(d): l.append(n)
    return l
print([n for n in primerange(2, 1001) if not B(n)]) # Indranil Ghosh, Jun 22 2017