A062285 -id:A062285 - cp's OEIS frontend

A030141 Numbers in which parity of the decimal digits alternates.

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

Offset: 1

Patrick De Geest

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

			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.

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.

Complement: A228709.
Subsequences: A030142, A030143, A030144, A030147, A030152, A062285.
Cf. A110303, A110304, A110305, A056830, A103181, A228722, A228723.

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

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 *)
Select[Range[0,150],FreeQ[Differences[Boole[EvenQ[IntegerDigits[#]]]],0]&] (* Harvey P. Dale, Jul 19 2025 *)

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

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

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

Offset corrected by Reinhard Zumkeller, Aug 31 2013

A030142 Odd numbers in which parity of digits alternates.

Original entry on oeis.org

1, 3, 5, 7, 9, 21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 101, 103, 105, 107, 109, 121, 123, 125, 127, 129, 141, 143, 145, 147, 149, 161, 163, 165, 167, 169, 181, 183, 185, 187, 189, 301, 303, 305, 307, 309, 321, 323

Offset: 1

Patrick De Geest

a(n) = A179085(n) for n <= 25. - Reinhard Zumkeller, Jun 28 2010

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A030143, A062285, intersection of A005408 and A030141.

a030142 n = a030142_list !! (n-1)
a030142_list = filter odd a030141_list
-- Reinhard Zumkeller, Aug 31 2013

id[n_]:=IntegerDigits[n];t={}; Do[If[Length[id[n]]==1, AppendTo[t,n], If[Union[Abs[Differences[Boole /@ EvenQ[id[n]]]]] == {1}, AppendTo[t,n]]], {n,1,323,2}]; t (* Jayanta Basu, May 07 2013 *)
Join[{1, 3, 5, 7, 9}, Select[Range[21, 323, 2], Total[Abs[Differences[Mod[(id = IntegerDigits[#]), 2]]]] == Length[id] - 1 &]] (* Zak Seidov, May 07 2013 *)

(a(n) mod 2) * A228710(a(n)) = 1. - Reinhard Zumkeller, Aug 31 2013

Offset corrected by Reinhard Zumkeller, Jun 28 2010

A030143 Even numbers in which parity of digits alternates.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 30, 32, 34, 36, 38, 50, 52, 54, 56, 58, 70, 72, 74, 76, 78, 90, 92, 94, 96, 98, 210, 212, 214, 216, 218, 230, 232, 234, 236, 238, 250, 252, 254, 256, 258, 270, 272, 274, 276, 278, 290, 292, 294, 296, 298, 410, 412, 414

Offset: 1

Patrick De Geest

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A030142, A062285, intersection of A005843 and A030141.

a030143 n = a030143_list !! (n-1)
a030143_list = filter even a030141_list
-- Reinhard Zumkeller, Aug 31 2013

id[n_]:=IntegerDigits[n]; t={}; Do[If[Length[id[n]]==1, AppendTo[t,n],If[Union[Abs[Differences[Boole /@ EvenQ[id[n]]]]]=={1}, AppendTo[t,n]]], {n,0,414,2}]; t (* Jayanta Basu, May 07 2013 *)

(1 - a(n) mod 2) * A228710(a(n)) = 1. - Reinhard Zumkeller, Aug 31 2013

Offset corrected by Reinhard Zumkeller, Aug 31 2013

A080467 Multiples of 11 in which the even positioned digits from left are odd and the odd positioned ones are even.

Original entry on oeis.org

0, 418, 616, 638, 814, 836, 858, 2101, 2123, 2145, 2167, 2189, 2321, 2343, 2365, 2387, 2541, 2563, 2585, 2761, 2783, 2981, 4103, 4125, 4147, 4169, 4301, 4323, 4345, 4367, 4389, 4521, 4543, 4565, 4587, 4741, 4763, 4785, 4961, 4983, 6105, 6127, 6149

Offset: 1

Amarnath Murthy, Mar 02 2003

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Intersection of A008593 and A062285.

Cf. A080466.

Terms corrected by Andrew Howroyd, Sep 29 2024

A376692 Numbers with the most significant digit odd and alternating parity of digits.

Original entry on oeis.org

1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 30, 32, 34, 36, 38, 50, 52, 54, 56, 58, 70, 72, 74, 76, 78, 90, 92, 94, 96, 98, 101, 103, 105, 107, 109, 121, 123, 125, 127, 129, 141, 143, 145, 147, 149, 161, 163, 165, 167, 169, 181, 183, 185, 187, 189, 301, 303, 305, 307, 309

Offset: 1

Andrew Howroyd, Oct 01 2024

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Complement of A062285 within A030141.

Cf. A030142, A030143, A080466.

isok(n)=my(d=digits(n)); for(i=1, #d, if((d[i]-i)%2, return(0))); 1

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A030141 Numbers in which parity of the decimal digits alternates.

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A030142 Odd numbers in which parity of digits alternates.

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A030143 Even numbers in which parity of digits alternates.

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A080467 Multiples of 11 in which the even positioned digits from left are odd and the odd positioned ones are even.

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A376692 Numbers with the most significant digit odd and alternating parity of digits.

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