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

1,1

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.

Links

Klaus Brockhaus, Table of n, a(n) for n=1..125

Eric Weisstein's World of Mathematics, Harshad Number

Example

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.

Prog

(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 */

Crossrefs

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

Sequence in context: A109016 A084025 A061157 * A026037 A266088 A122613

Adjacent sequences: A144375 A144376 A144377 * A144379 A144380 A144381

Keyword

base,hard,nonn

Author

Sergio Pimentel, Sep 18 2008

Extensions

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

Status

approved