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

1, 3, 6, 9, 12, 18, 27, 30, 36, 45, 54, 63, 81, 84, 90, 99, 108, 117, 135, 162, 171, 189, 216, 243, 246, 252, 261, 270, 279, 297, 324, 333, 351, 378, 405, 432, 486, 495, 513, 540, 567, 594, 648, 729, 732, 738, 747, 756, 765, 783, 810, 819, 837, 864, 891, 918, 972, 981, 999

Offset: 1

Author

Peter Luschny, Mar 08 2025

Keywords

• nonn
• base

Crossrefs

Cf. A007949, A053735.

Cf. A371176 (base 2), A381837 (base 4), A381836 (base 5).

Programs

Maple

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);

Mathematica

Select[Range[9000],DigitSum[#,3]Stefano Spezia, Mar 08 2025 *)

SageMath

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)]
print(aList(9000, 3))