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A357930
a(0) = 0; for n > 0, let S = concatenation of a(0)..a(n-1); a(n) is the number of times the digit at a(n-1) digits back from the end of S appears in S.
2
0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 7, 7, 8, 8, 7, 7, 8, 8, 7, 13, 7, 14, 7, 13, 13, 15, 15, 13, 15, 15, 6, 17, 16, 19, 8, 10, 10, 22, 10, 23
OFFSET
0,4
LINKS
Michael De Vlieger, Scalar scatterplot of a(n), n = 0..2^16, with points assigned a color function as to digit d that is a(n-1) digits back. Black indicates d=0, red d=1, ..., magenta d=9.
Michael De Vlieger, Log-log scatterplot of a(n), n = 0..2^20, with points assigned a color function as to digit d that is a(n-1) digits back. Black indicates d=0, red d=1, ..., magenta d=9.
EXAMPLE
a(7) = 3 as a(6) = 3 and the string concatenation of a(0)..a(6) = "0112223", and the digit 3 digits back from the end of the string concatenation is 2, and 2 has appeared three times in the string.
PROG
(MATLAB)
function a = A357930( max_n )
a = 0; s = '0'; c = zeros(1, 10); c(1) = 1;
for n = 2:max_n
k = c(s(end-a(n-1))-47); sk = num2str(k);
c(sk-47) = c(sk-47)+1; s = [s sk]; a(n) = k;
end
end % Thomas Scheuerle, Oct 21 2022
CROSSREFS
KEYWORD
nonn,base,look
AUTHOR
Scott R. Shannon, Oct 21 2022
STATUS
approved