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%I #33 Nov 13 2024 16:32:51
%S 7,8,12,13,15,16,18,24,26,28,31,32,36,40,42,48,54,56,57,60,62,63,64,
%T 70,72,76,80,84,88,90,93,96,98,100,108,112,114,120,121,124,126,127,
%U 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
%N 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.
%H Michael S. Branicky, <a href="/A377886/b377886.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 12 because 12 in base 5 is 22 where base 5 is a prime base and 5 < 12-1.
%t 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 *)
%o (Python)
%o from sympy import sieve
%o from sympy.ntheory import digits
%o def ok(n): return any(len(set(digits(n, p)[1:]))==1 for p in sieve.primerange(2, n-1))
%o print([k for k in range(253) if ok(k)]) # _Michael S. Branicky_, Nov 13 2024
%Y Cf. A125134.
%K nonn
%O 1,1
%A _Frank M Jackson_, Nov 12 2024