A258165 Odd non-Brazilian numbers > 1.

3, 5, 9, 11, 17, 19, 23, 25, 29, 37, 41, 47, 49, 53, 59, 61, 67, 71, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, 311, 313, 317, 331, 337

Offset: 1

Author

Daniel Lignon and Robert G. Wilson v, May 22 2015

Keywords

• nonn

Comments

Complement of A257521 in A144396 (odd numbers > 1).

The terms are only odd primes or squares of odd primes.

Most odd primes are present except those in A085104.

All terms which are not primes are squares of odd primes except 121 = 11^2.

Examples

			11 is present because there is no base b < 11 - 1 = 10 such that the representation of 11 in base b is a repdigit (all digits are equal). In fact, we have: 11 = 1011_2 = 102_3 = 23_4 = 21_5 = 15_6 = 14_7 = 13_8 = 12_9, and none of these representations are repdigits. - _Bernard Schott_, Jun 21 2017
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1150

Crossrefs

Cf. A085104, A125134, A190300, A220570, A220571, A220627, A242397, A253260, A253261, A257521.

Programs

Mathematica

fQ[n_] := Block[{b = 2}, While[b < n - 1 && Length@ Union@ IntegerDigits[n, b] > 1, b++]; b+1 == n]; Select[1 + 2 Range@ 170, fQ]

PARI

forstep(n=3, 300, 2, c=1; for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), c=0;  break));if(c,print1(n,", "))) \\ Derek Orr, May 27 2015

Python

from sympy.ntheory.factor_ import digits
l=[]
for n in range(3, 301, 2):
    c=1
    for b in range(2, n - 1):
        d=digits(n, b)[1:]
        if max(d)==min(d):
            c=0
            break
    if c: l.append(n)
print(l) # Indranil Ghosh, Jun 22 2017, after PARI program