cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A068134 Index of the smallest triangular number with digit sum = n-th triangular number.

Original entry on oeis.org

0, 1, 2, 3, 7, 12, 56, 109, 368, 1332, 5656, 28248, 140547, 774325, 8485151, 34339452, 397492132, 3996973827, 63229707890, 1039037824132, 10853561442116, 305279835527631, 4240235842471234, 117388244641426491, 3997445934568646292, 99999889989926488708
Offset: 0

Views

Author

Amarnath Murthy, Feb 21 2002

Keywords

Crossrefs

Cf. A068133.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 17 2002
a(18)-a(19) from Max Alekseyev, Jun 19 2011
a(0)=0 inserted by Sean A. Irvine, Jan 29 2024
a(20)-a(25) from Max Alekseyev, May 25 2025

A349875 Triangular numbers whose mean digit value reaches a new maximum.

Original entry on oeis.org

0, 1, 3, 6, 78, 686999778, 9876799878, 89996788896, 77779987999896, 589598998999878, 999699998689998991, 9988894989978899995, 95898999989999989765, 999999966989999986978996
Offset: 1

Views

Author

Jon E. Schoenfield, Dec 03 2021

Keywords

Comments

Subsequence of A068808.
No triangular number ends in 9, so the mean digit value is always less than 9.
Is this sequence finite? Or does the mean digit value approach some upper limit arbitrarily closely without ever reaching it exactly, and, if so, what is that limit?
a(14) <= 999999966989999986978996. - David A. Corneth, Dec 05 2021

Examples

			   n                  a(n)  digit sum  #dgts  mean digit value
  --  --------------------  ---------  -----  ----------------
   1                     0          0      1  0
   2                     1          1      1  1
   3                     3          3      1  3
   4                     6          6      1  6
   5                    78         15      2  7.5
   6             686999778         69      9  7.66666666666...
   7            9876799878         78     10  7.8
   8           89996788896         87     11  7.90909090909...
   9        77779987999896        111     14  7.92857142857...
  10       589598998999878        120     15  8
  11    999699998689998991        145     18  8.05555555555...
  12   9988894989978899995        154     19  8.10526315789...
  13  95898999989999989765        163     20  8.15
		

Crossrefs

Programs

  • Mathematica
    seq = {}; max = -1; Do[If[(m = Mean @ IntegerDigits[(t = n*(n + 1)/2)]) > max, max = m; AppendTo[seq, t]], {n, 0, 10^6}]; seq (* Amiram Eldar, Dec 03 2021 *)
  • Python
    def meandigval(n): s = str(n); return sum(map(int, s))/len(s)
    def afind(limit):
        alst, k, t, record = [], 0, 0, -1
        while t <= limit:
            mdv = meandigval(t)
            if mdv > record:
                print(t, end=", ")
                record = mdv
            k += 1
            t += k
    afind(10**14) # Michael S. Branicky, Dec 03 2021

Extensions

a(14) verified by Martin Ehrenstein, Dec 06 2021
Showing 1-2 of 2 results.