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

1,1

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A085104.

Sequence in context: A044042 A175179 A040060 * A040083 A045308 A245639

Adjacent sequences: A220624 A220625 A220626 * A220628 A220629 A220630

Keyword

nonn,base

Author

Bernard Schott, Dec 17 2012

Status

approved