A331009 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the n-th term and the n-th digit have the same parity.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 10, 31, 12, 33, 14, 35, 16, 37, 18, 39, 41, 20, 43, 45, 47, 22, 49, 51, 53, 24, 55, 57, 59, 26, 61, 63, 65, 28, 67, 69, 30, 71, 32, 34, 36, 73, 38, 75, 40, 77, 42, 44, 46, 79, 81, 83, 85, 87

Offset

1,2

Comments

This sequence is a variant of A324282; here we have equal parity, there different parity.

This sequence is a permutation of the natural numbers.

Links

Table of n, a(n) for n=1..67.

Rémy Sigrist, PARI program for A331009

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the corresponding digits, are:
  n   a(n)  n-th digit
  --  ----  ----------
   1     1           1
   2     2           2
   3     3           3
   4     4           4
   5     5           5
   6     6           6
   7     7           7
   8     8           8
   9     9           9
  10    11           1
  11    13           1
  12    15           1
  13    17           3
  14    19           1
  15    21           5

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[s=Array[a, n-1], k]||OddQ@k!= OddQ[Flatten[IntegerDigits/@Join[s, {k}]][[n]]], k++]; k); Array[a, 100] (* Giorgos Kalogeropoulos, Sep 07 2023 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A324282.

Sequence in context: A247945 A317621 A298297 * A225580 A071980 A058183

Adjacent sequences: A331006 A331007 A331008 * A331010 A331011 A331012

Keyword

nonn,base

Author

Rémy Sigrist, Jan 06 2020

Status

approved