A275776 The pair [a(n),a(n+1)] uses only one even digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 23, 33, 25, 35, 27, 37, 29, 39, 30, 51, 32, 53, 34, 55, 36, 57, 38, 59, 41, 71, 43, 73, 45, 75, 47, 77, 49, 79, 50, 91, 52, 93, 54, 95, 56, 97, 58, 99, 61, 111, 63, 113, 65, 115, 67, 117, 69, 119, 70, 131, 72, 133, 74, 135, 76, 137, 78, 139, 81, 151, 83, 153, 85, 155, 87, 157, 89, 159

Offset

1,2

Comments

The sequence starts with a(1) = 1 and was always extended with the smallest integer not yet used that doesn't lead to a contradiction.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

The pair [1,2] uses only one even digit (2).
The pair [2,3] uses only one even digit (2).
The pair [3,4] uses only one even digit (4).
The pair [4,5] uses only one even digit (4).
The pair [5,6] uses only one even digit (6).
The pair [6,7] uses only one even digit (6).
The pair [7,8] uses only one even digit (8).
The pair [8,9] uses only one even digit (8).
The pair [9,10] uses only one even digit (0).
The pair [10,11] uses only one even digit (0).
The pair [11,12] uses only one even digit (2).
etc.

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[Array[a, n-1], k]||Length@Select[Flatten[IntegerDigits/@{a[n-1], k}], EvenQ]!=1, k++]; k]; Array[a, 89] (* Giorgos Kalogeropoulos, May 12 2022 *)

Prog

(Python)
from itertools import islice
def one_even(s): return sum(1 for d in s if d in "02468") == 1
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 2
    while True:
        yield an
        k, stran = mink, str(an)
        while k in aset or not one_even(stran + str(k)): k += 1
        an = k
        aset.add(an)
        while mink in aset: mink += 1
print(list(islice(agen(), 89))) # Michael S. Branicky, May 12 2022

Crossrefs

Sequence in context: A052425 A272074 A246097 * A022465 A296762 A247751

Adjacent sequences: A275773 A275774 A275775 * A275777 A275778 A275779

Keyword

nonn,base

Author

Eric Angelini, Aug 08 2016

Status

approved