A033619 Undulating numbers (of form abababab... in base 10).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 111, 121, 131, 141, 151

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

References

• C. A. Pickover, "Keys to Infinity", Wiley 1995, p. 159,160.
• C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
• Eric Weisstein's World of Mathematics, Undulating Number

Crossrefs

Cf. A016073, A046075, A122875, A242541.

Programs

Haskell

import Data.Set (fromList, deleteFindMin, insert)
a033619 n = a033619_list !! (n-1)
a033619_list = [0..9] ++ (f $ fromList [10..99]) where
   f s = m : f (insert (m * 10 + h) s') where
     h = div (mod m 100) 10
     (m,s') = deleteFindMin s
-- Reinhard Zumkeller, May 01 2012

Maple

$0..9,seq(seq(seq(a*(10^(d+1)-10^(d+1 mod 2))/99 + b*(10^d - 10^(d mod 2))/99, b=0..9),a=1..9),d=2..6); # Robert Israel, Jul 08 2016

Mathematica

wave[1] = Range[0, 9]; wave[2] = Range[10, 99]; wave[n_] := wave[n] = Select[ Union[ Flatten[ {id = IntegerDigits[#]; FromDigits[ Prepend[id, id[[2]]]], FromDigits[ Append[id, id[[-2]]]]} & /@ wave[n-1]]], 10^(n-1) < # < 10^n & ]; Flatten[ Table[ wave[n], {n, 1, 3}]] (* Jean-François Alcover, Jun 19 2012 *)

Python

from itertools import count, islice
def agen(): # generator of terms
    yield from range(10)
    for d in count(2):
        q, r = divmod(d, 2)
        for a in "123456789":
            for b in "0123456789":
                yield int((a+b)*q + a*r)
print(list(islice(agen(), 106))) # Michael S. Branicky, Mar 28 2022