

A033619


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


9



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
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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. 123124, 316317.


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


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[n1]]], 10^(n1) < # < 10^n & ]; Flatten[ Table[ wave[n], {n, 1, 3}]] (* JeanFrançois Alcover, Jun 19 2012 *)


PROG

(Haskell)
import Data.Set (fromList, deleteFindMin, insert)
a033619 n = a033619_list !! (n1)
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


CROSSREFS

Sequence in context: A000027 A001477 A087156 * A130734 A244581 A090108
Adjacent sequences: A033616 A033617 A033618 * A033620 A033621 A033622


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



