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 A030141 Numbers in which parity of the decimal digits alternates. 36
 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 base-10, 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^n-1)/4. - Franklin T. Adams-Watters, 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 10-automatic sequences. EXAMPLE 121 is alternating and in the sequence because its consecutive digits are odd-even-odd, 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 !! (n-1) a030141_list = filter ((== 1) . a228710) [0..] -- Reinhard Zumkeller, Aug 31 2013 (PARI) is(n, d=digits(n))=for(i=2, #d, if((d[i]-d[i-1])%2==0, return(0))); 1 \\ Charles R Greathouse IV, Jul 08 2022 (Python) from itertools import count def A030141_gen(startvalue=0): # generator of terms >= startvalue return filter(lambda n:all(int(a)+int(b)&1 for a, b in zip(str(n), str(n)[1:])), count(max(startvalue, 0))) A030141_list = list(islice(A030141_gen(), 30)) # Chai Wah Wu, Jul 12 2022 (Python) from itertools import chain, count, islice def altgen(seed, digits): allowed = "02468" if seed in "13579" else "13579" if digits == 1: yield from allowed; return for f in allowed: yield from (f + r for r in altgen(f, digits-1)) def agen(): yield from chain(range(10), (int(f+r) for d in count(2) for f in "123456789" for r in altgen(f, d-1))) print(list(islice(agen(), 65))) # Michael S. Branicky, Jul 12 2022 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 A355596 A246077 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

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Last modified February 26 12:54 EST 2024. Contains 370352 sequences. (Running on oeis4.)