A358851 - OEIS

A358851

a(n+1) is the number of occurrences of the largest digit of a(n) among all the digits of [a(0), a(1), ..., a(n)], with a(0)=0.

0, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 11, 13, 2, 2, 3, 3, 4, 2, 4, 3, 5, 2, 5, 3, 6, 2, 6, 3, 7, 2, 7, 3, 8, 2, 8, 3, 9, 2, 9, 3, 10, 15, 4, 4, 5, 5, 6, 4, 6, 5, 7, 4, 7, 5, 8, 4, 8, 5, 9, 4, 9, 5, 10, 17, 6, 6, 7, 7, 8, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Up to a(19)=10, the terms are identical to A248034. The branches (distinct lines of terms indicating the largest digit of the preceding term) can be labeled by the counter digit (shown in the scatter plot). From 9 to 1 the branches gradually get fragmented. Below digit 5 it is harder to disentangle the branches in some places. A repeating pattern also appears (shown in the inset of the scatter plot).

LINKS

Bence Bernáth, Table of n, a(n) for n = 0..10000

Eric Angelini, Digit-counters updating themselves

Bence Bernáth, Scatter plot for n=0..500000

Michael De Vlieger, Log log scatterplot of a(n) n = 1..10^6.

Michael De Vlieger, Log log scatterplot of a(n), n = 1..10^5, with a color function indicating largest digit of preceding term, where black = 0, red = 1, orange = 2, ..., magenta = 9.

MATHEMATICA

nn = 79; s[_] = 0; a[0] = 0; Do[(Set[d, Max[#]]; Map[s[#1] += #2 & @@ # &, Tally[#] ]) &@ IntegerDigits[a[n - 1]]; a[n] = s[d], {n, nn}]; Array[a, nn + 1, 0] (* Michael De Vlieger, Dec 28 2022 *)

PROG

(MATLAB)

length_seq=150;

sequence(1)=0;

seq_for_digits=(num2str(sequence(1))-'0');

for i1=1:1:length_seq

sequence(i1+1)=sum(seq_for_digits==max((num2str(sequence(i1))-'0'))');

seq_for_digits=[seq_for_digits, num2str(sequence(i1+1))-'0'];

end

(Python)

sequence=[0]

length=150