The best definitions of the triple [this sequence,
A003157,
A003158] are as the rows a(n), b(n), c(n) of the table:
n: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
a: 1, 4, 5, 6, 9, 12, 15, 16, 17, 20, 21, 22, ...
b: 3, 8, 11, 14, 19, 24, 29, 32, 35, 40, 43, 46, ...
c: 2, 7, 10, 13, 18, 23, 28, 31, 34, 39, 42, 45, ...
where a(1)=1, b(1)=3, c(1)=2, and thereafter
a(n) = mex{a(i), b(i), c(i), i<n},
b(n) = a(n) + 2*n,
c(n) = b(n) - 1.
Then a,b,c form a partition of the positive integers.
Note that there is another triple of sequences (
A003144,
A003145,
A003146) also called a, b, c and also a partition of the positive integers, in a different paper by the same authors (Carlitz-Scovelle-Hoggatt) in the same volume of the same journal.
(End)
a(n) is the number of ones before the n-th zero in the Feigenbaum sequence
A035263. -
Philippe Deléham, Mar 27 2004
Number of odd numbers before the n-th even number in
A007413,
A007913,
A001511,
A029883,
A033485,
A035263,
A036585,
A065882,
A065883,
A088172,
A092412. -
Philippe Deléham, Apr 03 2004
Indices of a in the sequence closed under a -> abc, b -> a, c -> a, starting with a(1) = a; see
A092606 where a = 0, b = 2, c = 1. -
Philippe Deléham, Apr 12 2004
