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A381838 k/9 is in this list if A053735(k) < A007949(k), i.e. if digitsum(k, 3) < valuation(k, 3).

%I A381838 #11 Mar 09 2025 12:58:26
%S A381838 1,3,6,9,12,18,27,30,36,45,54,63,81,84,90,99,108,117,135,162,171,189,
%T A381838 216,243,246,252,261,270,279,297,324,333,351,378,405,432,486,495,513,
%U A381838 540,567,594,648,729,732,738,747,756,765,783,810,819,837,864,891,918,972,981,999
%N A381838 k/9 is in this list if A053735(k) < A007949(k), i.e. if digitsum(k, 3) < valuation(k, 3).
%p A381838 aList := upto -> local k; [seq(k/9, k in select(n -> add(convert(n, base, 3)) < padic[ordp](n, 3), [seq(9..upto,9)]))]: aList(9000);
%t A381838 Select[Range[9000],DigitSum[#,3]<IntegerExponent[#,3] &]/9 (* _Stefano Spezia_, Mar 08 2025 *)
%o A381838 (SageMath)
%o A381838 def aList(upto, b): return [n/b^2 for n in srange(b^2, upto, b^2) if sum(n.digits(b)) < valuation(n, b)]
%o A381838 print(aList(9000, 3))
%Y A381838 Cf. A007949, A053735.
%Y A381838 Cf. A371176 (base 2), A381837 (base 4), A381836 (base 5).
%K A381838 nonn,base
%O A381838 1,2
%A A381838 _Peter Luschny_, Mar 08 2025