A377886 Prime-based Brazilian numbers: numbers k such that there is a prime number p with 1 < p < k-1 such that the representation of k in base p has all equal digits.

7, 8, 12, 13, 15, 16, 18, 24, 26, 28, 31, 32, 36, 40, 42, 48, 54, 56, 57, 60, 62, 63, 64, 70, 72, 76, 80, 84, 88, 90, 93, 96, 98, 100, 108, 112, 114, 120, 121, 124, 126, 127, 128, 132, 133, 136, 140, 144, 148, 150, 152, 154, 156, 160, 162, 168, 171, 176, 180, 183, 186, 190, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 242, 248, 252

Offset

1,1

Links

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

Example

a(3) = 12 because 12 in base 5 is 22 where base 5 is a prime base and 5 < 12-1.

Mathematica

fQ[n_] :=  Module[{b=1}, While[Prime[b]<n-1&&Length[Union[IntegerDigits[n, Prime[b]]]]>1, b++]; Prime[b]<n-1]; Select[Range[4, 300], fQ](* after T. D. Noe in A125134 *)

Prog

(Python)
from sympy import sieve
from sympy.ntheory import digits
def ok(n): return any(len(set(digits(n, p)[1:]))==1 for p in sieve.primerange(2, n-1))
print([k for k in range(253) if ok(k)]) # Michael S. Branicky, Nov 13 2024

Crossrefs

Cf. A125134.

Sequence in context: A348784 A294483 A105740 * A050796 A106630 A050798

Adjacent sequences: A377883 A377884 A377885 * A377887 A377888 A377889

Keyword

nonn

Author

Frank M Jackson, Nov 12 2024

Status

approved