A372281 Numbers written in base of triangular numbers where the trailing digits are made as high as possible.

1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 18, 19, 27, 28, 29, 37, 38, 39, 47, 48, 49, 57, 58, 59, 67, 68, 69, 77, 78, 79, 87, 88, 89, 97, 98, 99, 187, 188, 189, 197, 198, 199, 287, 288, 289, 297, 298, 299, 387, 388, 389, 397, 398, 399, 487, 488, 489, 497, 498, 499, 587

Offset: 1

Author

Stefano Spezia, Apr 25 2024

Keywords

• nonn
• base
• easy

Comments

This sequence differs from A000462 whose leading digits are made as high as possible.

Examples

			The digits (from right to left) have values 1, 3, 6, 10, etc. (A000217), hence a(61) = 587 because 61 = 5*6 + 8*3 + 7*1.
		

Crossrefs

Cf. A000217, A000462.

9*A000292(n) gives the number of terms with at most n digits.

Programs

Mathematica

A000217[n_]:=n(n+1)/2; a[n_]:=Module[{s=0}, num=n; digits={}; s=Ceiling[Root[9(#1^3+3#1^2+2#1)-6num &, 1]]; While[s>0, AppendTo[digits, d=Ceiling[(num-9(s-1)^2)/A000217[s]]]; num-=d*A000217[s]; s--]; FromDigits[digits]]; Array[a,61]