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

11, 22, 37, 136, 13, 64, 73, 163, 91, 1730, 289, 1639, 379, 1660, 2737, 919, 559, 14878, 7561, 5671, 9753, 2890, 7777, 4888, 5785, 5590, 27973, 47872, 28681, 22681, 3785, 36184, 46281, 71281, 6481, 48952, 48763, 64978, 119773, 69782, 77881, 55973

Offset: 1

Author

Sergio Pimentel, Sep 18 2008

Keywords

• base
• hard
• nonn

Comments

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.

Many terms end in '81' for some reason.

This sequence is analog to A060159 with non-Niven numbers.

This sequence is infinite, as opposed as A060159.

Examples

			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.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n=1..125
• Eric Weisstein's World of Mathematics, Harshad Number

Crossrefs

Cf. A005349, A082516, A060159, A144261, A144262.

Programs

PARI

digitsum(n) = {local(s=0); while(n, s+=n%10; n\=10); s}
{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 */

Extensions

a(2), a(22), a(42) corrected by Klaus Brockhaus, Sep 24 2008