A000462 Numbers written in base of triangular numbers.

1, 2, 10, 11, 12, 100, 101, 102, 110, 1000, 1001, 1002, 1010, 1011, 10000, 10001, 10002, 10010, 10011, 10012, 100000, 100001, 100002, 100010, 100011, 100012, 100100, 1000000, 1000001, 1000002, 1000010, 1000011, 1000012, 1000100, 1000101, 10000000, 10000001

Offset: 1

Author

John Radu (Suttones(AT)aol.com)

Keywords

• nonn
• base
• easy

Comments

A003056 and A057945 give lengths and sums. - Reinhard Zumkeller, Mar 27 2011

Examples

			The digits (from right to left) have values 1, 3, 6, 10, etc. (A000217), hence a(20) = 10012 because 20 = 1*15 + 0*10 + 0*6 + 1*3 + 2*1. - _Stefano Spezia_, Apr 25 2024
		

References

• F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 237-240.
• F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
• Eric Weisstein's World of Mathematics, Smarandache Sequences.

Crossrefs

Cf. A000217, A003056, A057945.

Programs

Haskell

a000462 n = g [] n $ reverse $ takeWhile (<= n) $ tail a000217_list where
   g as 0 []     = read $ concat $ map show $ reverse as :: Integer
   g as x (t:ts) = g (a:as) r ts where (a,r) = divMod x t
-- Reinhard Zumkeller, Mar 27 2011

Mathematica

A000217[n_]:=n(n+1)/2; a[n_]:=Module[{k=0}, num=n; digits={}; k=Floor[(Sqrt[1+8num]-1)/2]; While[num>0, AppendTo[digits, Floor[num/A000217[k]]]; num=Mod[num, A000217[k]]; kold=k; k=Floor[(Sqrt[1+8num]-1)/2]; While[kStefano Spezia, Apr 25 2024 *)