

A143232


Sum of denominators of Egyptian fraction expansion of A004001(n)  n/2.


1



2, 0, 2, 0, 2, 1, 2, 0, 2, 1, 3, 1, 3, 1, 2, 0, 2, 1, 3, 2, 3, 2, 4, 2, 4, 2, 3, 2, 3, 1, 2, 0, 2, 1, 3, 2, 4, 2, 4, 3, 5, 3, 5, 4, 5, 4, 5, 3, 5, 4, 5, 4, 5, 3, 5, 3, 4, 2, 4, 2, 3, 1, 2, 0, 2, 1, 3, 2, 4, 3, 4, 3, 5, 4, 6, 4, 6, 5, 7, 5, 7, 6, 7, 6, 7, 5, 7, 6, 8, 6, 8, 7, 8, 7, 8, 6, 8, 7, 8, 7, 8, 6, 8, 6, 7
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OFFSET

1,1


COMMENTS

A004001 is the HofstadterConway $10,000 Sequence and A004001(n)  n/2 is increasingly larger versions of the batrachion Blancmange function.


LINKS



FORMULA

a(n) = Sum of denominators of Egyptian fraction expansion of A004001(n)  n/2 .
For practical purposes, a full Egyptian fraction algorithm is not necessary. Since the elements of A004001(n)  n/2 are either whole or their fractional part is .5, the sequence can be effected by a(n) = sefd(A004001(n)  n/2) with sefd(x) = x + 3 * (x  floor(x)) .


EXAMPLE

a(43) = 5 because A004001(43) = 25, so (A004001(43)  (43/2)) = 3.5 and the Egyptian fraction expansion of 3.5 is (1/1)+(1/1)+(1/1)+(1/2), so the denominators are 1,1,1,2 which sums to 5.


PROG

(J) a004001 =: ((] +&:$: ) $:@:<:)@.(2&<) M.
a143232 =: (+ 3 * 1&)@:(a004001  :)"0


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

Dan Bron (j (at) bron.us), Jul 31 2008


STATUS

approved



