OFFSET
1,6
COMMENTS
The first time a number appears for the 8th time is a(1491228545) = 953950324. - Pontus von Brömssen, Jul 06 2023
LINKS
Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Thomas Scheuerle, Scatterplot of a(n)/n for the first 100000 values. It is remarkable that we see extreme values a(n)/n > 0.99 for n = {1, 20957, 22061, 24915, ...}.
Neal Gersh Tolunsky, Graph of first 500000 terms
EXAMPLE
a(8)=5 occurs two times, so a(9) is the number of terms which do not occur two times, which is 4 (there are three 0s and one 2).
MATHEMATICA
a[1] = 1; a[n_] := a[n] = Total[Select[Tally[v = Array[a, n - 1]][[;; , 2]], # != Count[v, a[n - 1]] &]]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)
PROG
(Python)
from itertools import count, islice
from collections import defaultdict
def A363764_gen():
x = 1
freq = defaultdict(int)
freq[x] = f0 = 1
freqfreq = defaultdict(int)
freqfreq[1] = 1
for n in count(1):
yield x
x = n-f0*freqfreq[f0]
freq[x] = f0 = freq[x]+1
if f0 != 1: freqfreq[f0-1] -= 1
freqfreq[f0] += 1
def A363764_list(nmax):
return list(islice(A363764_gen(), nmax)) # Pontus von Brömssen, Jul 01 2023 (after an idea by Kevin Ryde)
(MATLAB)
function a = A363764( max_n )
s = zeros(1, max_n); a = 1; s(2) = 1;
for n = 2:max_n
a(n) = length(find(s(a+1)~=s(a(n-1)+1)));
s(a(n)+1) = s(a(n)+1)+1;
end
end % Thomas Scheuerle, Jun 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Jun 28 2023
STATUS
approved