cp's OEIS Frontend

A326834 a(0) = 0; a(1) = 0; for n > 0, a(n) = the sum of the number of times each digit in a(n-1) has occurred from a(0) to a(n-2) inclusive.

%I A326834 #29 Mar 24 2025 11:40:01
%S A326834 0,0,1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,0,10,12,3,1,3,2,2,3,3,4,1,4,2,
%T A326834 4,3,5,1,5,2,5,3,6,1,6,2,6,3,7,1,7,2,7,3,8,1,8,2,8,3,9,1,9,2,9,3,10,
%U A326834 22,20,25,17,15,17,18,18,20,28,21,32,28,25,25,27
%N A326834 a(0) = 0; a(1) = 0; for n > 0, a(n) = the sum of the number of times each digit in a(n-1) has occurred from a(0) to a(n-2) inclusive.
%C A326834 This sequence sums the previous digits the same way as A309261, except that here digits in a(n-1) are not considered unique, so each digit in a(n-1) is summed regardless of the number of times it appears in a(n-1). This leads to this sequence being the same as A309261 up to a(66) = 22, after which they diverge.
%H A326834 Scott R. Shannon, <a href="/A326834/b326834.txt">Table of n, a(n) for n = 0..19999</a>
%H A326834 Scott R. Shannon, <a href="/A326834/a326834_1.png">Plot of a(n) for n = 0..10^6</a> [This is a dramatic graph - _N. J. A. Sloane_, Oct 21 2019]
%e A326834 a(2) = 1, as a(1) = 0, and '0' has occurred one previous time in the sequence before a(1).
%e A326834 a(62) = 2, as a(61) = 9, and '9' has occurred two previous times. '2' has now occurred 10 times in the sequence.
%e A326834 a(66) = 22, as a(65) = 10, and '1' has occurred ten previous times, and '0' has occurred twelve previous times, and 10 + 12 = 22.
%e A326834 a(67) = 20, as a(66) = 22, and '2' has occurred ten previous times, and '2' has occurred ten previous times, and 10 + 10 = 20.
%o A326834 (Python)
%o A326834 from collections import Counter
%o A326834 from itertools import count, islice
%o A326834 def agen(): # generator of terms
%o A326834     an, c = 0, Counter()
%o A326834     while True:
%o A326834         yield an
%o A326834         s = str(an)
%o A326834         an = sum(c[d] for d in s)
%o A326834         c.update(s)
%o A326834 print(list(islice(agen(), 82))) # _Michael S. Branicky_, Mar 24 2025
%Y A326834 Cf. A004207, A309261.
%K A326834 nonn,look,base
%O A326834 0,5
%A A326834 _Scott R. Shannon_, Oct 20 2019