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
More terms from Larry Reeves (larryr(AT)acm.org), Jun 17 2002
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
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
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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 *)
-
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
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