Puzzle sequence and A109652
Joseph Biberstine
jrbibers at indiana.edu
Sun Aug 6 04:47:34 CEST 2006
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While toying with the puzzle seq I came across A109652, which appears
to be inconsistent with its definition. Depending on the offset, my
interpretation of the definition, and Cloitre's formula, one would
expect at least one of the following sequences to be all zero:
A3849(A109652 - 2) = {0, 0, 0, 0, 1, ...}
A3849(A109652 - 1) = {1, 1, ...}
A3849(A109652) = {0, 0, 0, 0, 1, ...}
A3849(A109652 + 1) = {0, 1, 0, ...}
A3849(A109652 + 2) = {1, 0, 1, 0, ...}
These were calculated using the following formula from A3849:
"a(n) = floor((n+2)*r)-floor((n+1)*r) where r=phi/(1+2*phi) and phi is
the Golden Ratio. - Benoit Cloitre (abmt(AT)wanadoo.fr), Nov 10 2003"
*However*, a fitting definition for A109652 seems to be A40(A201). All
terms agree.
- JRB
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