

A030141


Numbers in which parity of the decimal digits alternates.


30



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 101, 103, 105, 107, 109, 121, 123, 125, 127, 129
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

An alternating integer is a positive integer for which, in base10, the parity of its digits alternates.
The number of terms < 10^n (n>=0): 1, 10, 55, 280, 1405, 7030, 35155, ..., .  Robert G. Wilson v, Apr 01 2011
The number of terms between 10^n and 10^(n+1) is 9 * 5^n for n>=0. For n>=0, number of terms < 10^n is 1 + 9 * (5^n1)/4.  Franklin T. AdamsWatters, Apr 01 2011
A228710(a(n)) = 1.  Reinhard Zumkeller, Aug 31 2013


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
45th International Mathematical Olympiad (45th IMO), Problem #6 and Solution, Mathematics Magazine, 78 (2005), pp. 247, 250, 251.
Index entries for 10automatic sequences.


EXAMPLE

121 is alternating and in the sequence because its consecutive digits are oddevenodd, 1 being odd and 2 even. Of course, 1234567890 is also alternating.


MATHEMATICA

fQ[n_] := Block[{m = Mod[ IntegerDigits@ n, 2]}, m == Split[m, UnsameQ][[1]]]; Select[ Range[0, 130], fQ] (* Robert G. Wilson v, Apr 01 2011 *)


PROG

(Haskell)
a030141 n = a030141_list !! (n1)
a030141_list = filter ((== 1) . a228710) [0..]
 Reinhard Zumkeller, Aug 31 2013


CROSSREFS

Complement: A228709.
Subsequences: A030142, A030143, A030144, A030147, A030152, A062285.
Cf. A110303, A110304, A110305, A056830, A103181, A228722, A228723.
Sequence in context: A103969 A271168 A292514 * A242367 A246077 A064915
Adjacent sequences: A030138 A030139 A030140 * A030142 A030143 A030144


KEYWORD

nonn,base,easy


AUTHOR

Patrick De Geest


EXTENSIONS

Offset corrected by Reinhard Zumkeller, Aug 31 2013


STATUS

approved



