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%I #26 Apr 25 2024 13:41:09
%S 1,2,10,11,12,100,101,102,110,1000,1001,1002,1010,1011,10000,10001,
%T 10002,10010,10011,10012,100000,100001,100002,100010,100011,100012,
%U 100100,1000000,1000001,1000002,1000010,1000011,1000012,1000100,1000101,10000000,10000001
%N Numbers written in base of triangular numbers.
%C A003056 and A057945 give lengths and sums. - _Reinhard Zumkeller_, Mar 27 2011
%D F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.
%H Reinhard Zumkeller, <a href="/A000462/b000462.txt">Table of n, a(n) for n = 1..10000</a>
%H F. Iacobescu, <a href="http://fs.unm.edu/FANELI.HTM">Smarandache Partition Type and Other Sequences</a>, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 237-240.
%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">Sequences of Numbers Involved in Unsolved Problems</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>.
%e 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
%t 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 *)
%o (Haskell)
%o a000462 n = g [] n $ reverse $ takeWhile (<= n) $ tail a000217_list where
%o g as 0 [] = read $ concat $ map show $ reverse as :: Integer
%o g as x (t:ts) = g (a:as) r ts where (a,r) = divMod x t
%o -- _Reinhard Zumkeller_, Mar 27 2011
%Y Cf. A000217, A003056, A057945.
%K nonn,base,easy,changed
%O 1,2
%A John Radu (Suttones(AT)aol.com)
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