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A276134 a(5n) = a(n), a(5n+1) = a(5n+2) = a(5n+3) = a(5n+4) = a(n) + 1, a(0) = 0.

%I A276134 #18 Sep 08 2016 09:31:25
%S A276134 0,1,1,1,1,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,2,3,3,3,
%T A276134 3,2,3,3,3,3,2,3,3,3,3,2,3,3,3,3,1,2,2,2,2,2,3,3,3,3,2,3,3,3,3,2,3,3,
%U A276134 3,3,2,3,3,3,3,1,2,2,2,2,2,3,3,3,3,2,3,3,3,3,2,3,3,3,3,2,3,3,3,3,1,2,2,2,2,2,3,3,3,3,2,3,3,3,3,2,3,3,3,3,2
%N A276134 a(5n) = a(n), a(5n+1) = a(5n+2) = a(5n+3) = a(5n+4) = a(n) + 1, a(0) = 0.
%C A276134 Number of nonzero digits in the base 5 representation of n.
%C A276134 Fixed point of the mapping 0 -> 01111, 1 -> 12222, 2 -> 23333, ...
%C A276134 Self-similar or fractal sequence (underlining every fifth term, reproduce the original sequence).
%H A276134 Robert Israel, <a href="/A276134/b276134.txt">Table of n, a(n) for n = 0..10000</a>
%H A276134 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%H A276134 Ilya Gutkovskiy, <a href="/A276134/a276134.jpg">Illustration (mapping 0 -> 01111, 1 -> 12222, 2 -> 23333, ...)</a>
%F A276134 a(5^k) = 1.
%F A276134 a(5^k-1) = k.
%F A276134 a(5^k-m) = k, k>0, m = 2,3,4.
%F A276134 a(5^k+m) = 2, k>0, m = 1,2,3,4.
%F A276134 a(5^k-a(5^k)) = k.
%F A276134 a(5^k+(-1)^k) = (k + (-1)^k*(k - 1) + 3)/2.
%F A276134 a(5^k+(-1)^k-1) = A093178(k).
%F A276134 a(5^k+(-1)^k+1) = A000034(k+1), k>0.
%F A276134 G.f. g(x) satisfies g(x) = (1+x+x^2+x^3+x^4)*g(x^5) + (x+x^2+x^3+x^4)/(1-x^5). - _Robert Israel_, Sep 07 2016
%e A276134 The evolution starting with 0 is: 0 -> 01111 -> 0111112222122221222212222 -> ...
%e A276134 ...
%e A276134 a(0) = 0;
%e A276134 a(1) = a(5*0+1) = a(0) + 1 = 1;
%e A276134 a(2) = a(5*0+2) = a(0) + 1 = 1;
%e A276134 a(3) = a(5*0+3) = a(0) + 1 = 1;
%e A276134 a(4) = a(5*0+4) = a(0) + 1 = 1;
%e A276134 a(5) = a(5*1+0) = a(1) = 1;
%e A276134 a(6) = a(5*1+1) = a(1) + 1 = 2, etc.
%e A276134 ...
%e A276134 Also a(10) = 1, because 10 (base 10) = 20 (base 5) and 20 has 1 nonzero digit.
%p A276134 f:= n -> nops(subs(0=NULL,convert(n,base,5))):
%p A276134 map(f, [$0..100]); # _Robert Israel_, Sep 07 2016
%t A276134 Join[{0}, Table[IntegerLength[n, 5] - DigitCount[n, 5, 0], {n, 120}]]
%Y A276134 Cf. A000034, A000120, A093178, A160384, A160385.
%K A276134 nonn,base,look
%O A276134 0,7
%A A276134 _Ilya Gutkovskiy_, Aug 21 2016