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A324400
Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = -1 if n = 2^k and k > 0, and f(n) = n for all other numbers.
57
1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 2, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78
OFFSET
1,2
COMMENTS
In the following, A stands for this sequence, A324400, and S -> T (where S and T are sequence A-numbers) indicates that for all i, j >= 1: S(i) = S(i) => T(i) = T(j).
For example, the following chains of implications hold:
A -> A286619 -> A005811,
and
A -> A003602 -> A286622 -> A000120,
-> A323889,
-> A000593,
-> A001227,
among many others.
LINKS
FORMULA
If n <= 3, a(n) = n; and for n >= 4, if A209229(n) = 1, then a(n) = 2, otherwise a(n) = 1 + n - A000523(n).
PROG
(PARI)
A000523(n) = if(n<1, 0, #binary(n)-1);
A324400(n) = if(n<4, n, if(!bitand(n, n-1), 2, 1+n-A000523(n)));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 01 2019
STATUS
approved