A129120 Undulating Harshad numbers: numbers divisible by the sum of their own digits with decimal expansions in an abab...ab pattern.

10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 171, 252, 414, 828, 1010, 1212, 1818, 2020, 2424, 3030, 3636, 4040, 4848, 5050, 5454, 6060, 7070, 7272, 8080, 9090, 10101, 13131, 20202, 23232, 26262, 30303, 39393

Offset: 1

Author

Jason Earls, May 25 2007

Keywords

• base
• nonn

Comments

This definition of "undulating" is more restrictive than the one used in A033619 and excludes single-digit numbers and numbers of the pattern aaaaaa. - R. J. Mathar, Jun 15 2007

References

• Jason Earls, Red Zen, Lulu Press, NY, 2006, pp. 56-57. ISBN: 978-1-4303-2017-3.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2146

Crossrefs

Cf. A005349, A033619.

Programs

Mathematica

undHarsQ[n_] := Module[{d = IntegerDigits[n]}, Divisible[n, Plus @@ d] &&  Length @ Union[d] > 1 && Length @ Union[d[[1 ;; -1 ;; 2]]] == 1 && Length @ Union[d[[2 ;; -1 ;; 2]]] == 1 ]; Select[Range[40000], undHarsQ] (* Amiram Eldar, Jan 27 2021 *)

Extensions

More terms from R. J. Mathar, Jun 15 2007