A118388 Least k such that T(k) includes the consecutive digits of n, where T(k) = k*(k+1)/2.

0, 1, 6, 2, 9, 5, 3, 12, 7, 13, 4, 47, 15, 16, 53, 5, 57, 18, 60, 19, 15, 6, 49, 21, 69, 22, 51, 23, 7, 76, 24, 21, 25, 81, 68, 26, 8, 27, 87, 88, 28, 38, 92, 29, 94, 9, 30, 97, 54, 31, 75, 26, 32, 17, 55, 10, 33, 84, 108, 34, 79, 33, 72, 35, 113, 30, 11, 106, 183

Offset

0,3

Comments

The T(k) for each n are at A118389.

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Example

====================
n k T(k)
====================
0 0 0
1 1 1
2 6 21
3 2 3
4 9 45
5 5 15
6 3 6
7 12 78
8 7 28
9 13 91
10 4 10

Mathematica

nn = 68; t = Table[0, {nn}]; n = 0; found = 0; While[found < nn, n++; k = n (n + 1)/2; d = IntegerDigits[k]; s = Sort[FromDigits /@ Flatten[Table[Partition[d, i, 1], {i, Length[d]}], 1]]; i = 1; While[i <= Length[s] && s[[i]] <= nn, If[t[[s[[i]]]] == 0, t[[s[[i]]]] = n; found++]; i++]]; t = Join[{0}, t] (* T. D. Noe, Sep 03 2013 *)
Module[{tn=Accumulate[Range[200]], trms}, trms=Table[SelectFirst[ tn, SequenceCount[ IntegerDigits[ #], IntegerDigits[n]]>0&], {n, 70}]; Join[ {0}, (Sqrt[8#+1]-1)/2&/@trms]] (* Harvey P. Dale, Aug 02 2021 *)

Crossrefs

Cf. A000217, A118389.

Sequence in context: A100123 A228040 A153633 * A213913 A195491 A243453

Adjacent sequences: A118385 A118386 A118387 * A118389 A118390 A118391

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Apr 26 2006

Extensions

Corrected by T. D. Noe, Sep 03 2013

Status

approved