OFFSET
1,3
COMMENTS
The sequence starts with a(1) = 1 and was always extended with the smallest nonnegative integer not yet present that does not lead to a contradiction.
Sequence places odd numbers (2n - 1) at position A002061(n). First even number to appear after this is A001105(n - 1). - Michael De Vlieger, Oct 12 2016
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..7162
FORMULA
a(m*(m+1) + 1) = 2m + 1 for m > 0. - David A. Corneth, Oct 11 2016
EXAMPLE
As a(1) = 1, we take for a(2) the even integer "0"; we then extend the sequence with a(3) which must be the smallest odd integer not yet present: this is "3"; we take for a(4), a(5) and a(6) the 3 smallest even integers not yet present: they are 2, 4 and 6; we then extend the sequence with the smallest odd available integer, which is a(7) = 5. Etc.
MATHEMATICA
Table[Prepend[2 Range[#^2, #^2 + 2 n - 2] &@ (n - 1), 2 n - 1], {n, 9}] // Flatten (* Michael De Vlieger, Oct 12 2016 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Oct 11 2016
STATUS
approved