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A144378 Initial term of a series of exactly n consecutive non-Niven (or Harshad) numbers.

%I A144378 #9 Feb 16 2025 08:33:09
%S A144378 11,22,37,136,13,64,73,163,91,1730,289,1639,379,1660,2737,919,559,
%T A144378 14878,7561,5671,9753,2890,7777,4888,5785,5590,27973,47872,28681,
%U A144378 22681,3785,36184,46281,71281,6481,48952,48763,64978,119773,69782,77881,55973
%N A144378 Initial term of a series of exactly n consecutive non-Niven (or Harshad) numbers.
%C A144378 Multiples of 18 seem to be the high water marks, while terms of the form 18n - 1 seem to be the valleys of this sequence.
%C A144378 Many terms end in '81' for some reason.
%C A144378 This sequence is analog to A060159 with non-Niven numbers.
%C A144378 This sequence is infinite, as opposed as A060159.
%H A144378 Klaus Brockhaus, <a href="/A144378/b144378.txt">Table of n, a(n) for n=1..125</a>
%H A144378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarshadNumber.html">Harshad Number</a>
%e A144378 a(5) = 13 since 13, 14, 15, 16 and 17 are all non-Niven numbers and this is the first occurrence of exactly 5 non-Niven numbers.
%o A144378 (PARI) digitsum(n) = {local(s=0); while(n, s+=n%10; n\=10); s}
%o A144378 {m=120000; z=42; w=vector(z); n=1; while(n<=m, while(n%digitsum(n)==0, n++); a=n; c=0; while(n%digitsum(n)>0, n++; c++); if(c<=z&&w[c]==0, w[c]=a)); j=1; while(j<=z&&w[j]>0, print1(w[j], ","); j++)} /* _Klaus Brockhaus_, Sep 24 2008 */
%Y A144378 Cf. A005349, A082516, A060159, A144261, A144262.
%K A144378 base,hard,nonn
%O A144378 1,1
%A A144378 _Sergio Pimentel_, Sep 18 2008
%E A144378 a(2), a(22), a(42) corrected by _Klaus Brockhaus_, Sep 24 2008