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

1,2

Comments

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

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.

Example

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

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[k<kold-1, AppendTo[digits, 0]; kold--]]; FromDigits[digits]]; Array[a, 37] (* Stefano Spezia, Apr 25 2024 *)

Prog

(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

Crossrefs

Cf. A000217, A003056, A057945.

Sequence in context: A134948 A060045 A340051 * A340649 A309942 A282093

Adjacent sequences: A000459 A000460 A000461 * A000463 A000464 A000465

Keyword

nonn,base,easy

Author

John Radu (Suttones(AT)aol.com)

Status

approved