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A180160 (sum of digits) mod (number of digits) of n in decimal representation.

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%I A180160 #10 Jul 30 2025 16:43:13
%S A180160 0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,
%T A180160 1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,
%U A180160 0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,2,0,1,2
%N A180160 (sum of digits) mod (number of digits) of n in decimal representation.
%C A180160 a(n) = A007953(n) mod A055642(n);
%C A180160 a(A061383(n)) = 0; a(A180157(n)) > 0;
%C A180160 a(repdigits)=0: a(A010785(n))=0: a(A002275(n))=0: a(A002276(n))=0: a(A002277(n))=0: a(A002278(n))=0: a(4(n))=0: a(A002279(n))=0: a(A002280(n))=0: a(A002281(n))=0: a(A002282(n))=0: a(A002283(n))=0;
%C A180160 A123522 gives smallest m such that a(m) = n.
%H A180160 Reinhard Zumkeller, <a href="/A180160/b180160.txt">Table of n, a(n) for n = 0..25000</a>
%t A180160 A180160[n_] := If[n == 0, 0, Mod[Total[#], Length[#]] & [IntegerDigits[n]]];
%t A180160 Array[A180160, 100, 0] (* _Paolo Xausa_, Jun 30 2024 *)
%t A180160 Join[{0},Table[Mod[Total[IntegerDigits[n]],IntegerLength[n]],{n,110}]] (* _Harvey P. Dale_, Jul 30 2025 *)
%Y A180160 Cf. A002275-A002283, A007953, A010785, A055642, A061383, A123522, A180157, A374097.
%K A180160 base,nonn
%O A180160 0,102
%A A180160 _Reinhard Zumkeller_, Aug 15 2010