A258165 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

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]

PROG

(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