cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A087143 Numbers n such that sum of digits of n is divisible by digital root of n.

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%I A087143 #13 Oct 13 2022 11:12:06
%S A087143 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A087143 27,28,30,31,32,33,34,35,36,37,39,40,41,42,43,44,45,46,48,50,51,52,53,
%U A087143 54,55,57,60,61,62,63,64,66,70,71,72,73,75,80,81,82,84,90
%N A087143 Numbers n such that sum of digits of n is divisible by digital root of n.
%C A087143 A007953(a(n)) mod A010888(a(n)) = 0; multiples of 9 are a subsequence (A008591, n>0).
%H A087143 Nathaniel Johnston, <a href="/A087143/b087143.txt">Table of n, a(n) for n = 1..10000</a>
%e A087143 84 is a term because 12 (its sum of digits) is divisible by 3 (its digital root).
%p A087143 A087143 := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(add(d, d=convert(k,base,10)) mod (((k-1) mod 9) + 1) = 0)then return k: fi: od: end: seq(A087143(n),n=1..100); # _Nathaniel Johnston_, May 05 2011
%t A087143 sddrQ[n_]:=Module[{sd=Total[IntegerDigits[n]],dr},dr=sd;While[dr>9, dr= Total[ IntegerDigits[dr]]];Divisible[sd,dr]]; Select[Range[100],sddrQ] (* _Harvey P. Dale_, May 22 2013 *)
%o A087143 (PARI) is(n)=sumdigits(n)%((n-1)%9+1) == 0 \\ _Charles R Greathouse IV_, Oct 13 2022
%Y A087143 Complement of A087144.
%Y A087143 Cf. A010888, A064807.
%K A087143 nonn,easy,base
%O A087143 1,2
%A A087143 _Reinhard Zumkeller_, Aug 18 2003