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

1,3

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A016073, A046075, A122875, A242541.

Sequence in context: A292579 A262530 A291179 * A130734 A118759 A258069

Adjacent sequences: A033616 A033617 A033618 * A033620 A033621 A033622

Keyword

nonn,base,easy

Author

N. J. A. Sloane.

Status

approved