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

1,1

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

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 *)

Crossrefs

Cf. A005349, A033619.

Sequence in context: A247626 A247627 A327709 * A134516 A144363 A051247

Adjacent sequences: A129117 A129118 A129119 * A129121 A129122 A129123

Keyword

base,nonn

Author

Jason Earls, May 25 2007

Extensions

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

Status

approved