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A375863
a(1) = 0 and a(n) = A050603(n-1)^2 for n > 0. Lexicographically earliest nonnegative sequence of integers such that the Gilbreath transform of a(1..n) gives floor(log_2(n)).
0
0, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 16, 16, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 25, 25, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 16, 16, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 36, 36, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 16, 16, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 25
OFFSET
1,4
EXAMPLE
The first row is the sequence itself. The rows below are the absolute differences
of each previous row:
0, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 16, 16, ...
1, 0, 3, 0, 3, 0, 8, 0, 8, 0, 3, 0, 3, 0, 15, 0, ...
1, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 15, 15, ...
2, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 12, 0, ...
2, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 12, 12, ...
2, 0, 5, 0, 5, 0, 5, 0, 5, 0, 12, 0, ...
2, 5, 5, 5, 5, 5, 5, 5, 5, 12, 12, ...
3, 0, 0, 0, 0, 0, 0, 0, 7, 0, ...
3, 0, 0, 0, 0, 0, 0, 7, 7, ...
3, 0, 0, 0, 0, 0, 7, 0, ...
3, 0, 0, 0, 0, 7, 7, ...
3, 0, 0, 0, 7, 0, ...
3, 0, 0, 7, 7, ...
3, 0, 7, 0, ...
3, 7, 7, ...
4, 0, ...
4, ...
The main diagonal is floor(log_2(n)), where n = 1 in the first row and n = 2 in the second etc. .
PROG
(PARI) a(n) = if(n == 1, 0, valuation(n-(n-2)%2, 2)^2)
CROSSREFS
Cf. A050603, A039963 (Gilbreath transform of floor(log_2(n))).
Sequence in context: A046539 A198929 A172347 * A108428 A373431 A174126
KEYWORD
nonn
AUTHOR
Thomas Scheuerle, Sep 02 2024
STATUS
approved