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.

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

Author

Scott R. Shannon, Oct 21 2022

Keywords

• nonn
• base
• look

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..9999
• Michael De Vlieger, Table of n, a(n) for n = 0..10^5
• 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.
• Scott R. Shannon, Image of the first 5000000 terms.

Crossrefs

Cf. A117707, A356348, A000217, A351753.

Programs

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