[seqfan] Re: A061653 offset

[Maximilian Hasler]

On Tue, Feb 3, 2009 at 8:38 PM, Tanya Khovanova wrote:
> I keep being confused with offsets. Should the offset for A061653 be 2?
> It starts with n=2.

Yes... some formulae would be useful for cross checking.
In fact there are several inconsistencies *and* errors related to
A061494 , A061653 , A042965
that go beyond changing an offset/

Maybe some resulted from the 2007 edit of A042965 (it is not said what
that edit was, but it might have been a change of offset from 0 to 1).
[*]
[* I found the SeqFan discussion, entitled "possibly double", which
seems having ended in merging data from A074227 (now dead) into
A042965 ; this seems to include some of the now a bit obscure code
(very complicated way to print out numbers 1,3,4,5,7,...) -- however
A074227 started with offset 1.]

The problem might be that both A061494 and A042965 are lists of
numbers and thus should start with offset 1, but A042965 starts with 0
while A061653 is/seems not defined at 0 (?convention?) so the formula
one would like to have,
%F A061494 a(n) = A061653( A042965( n ))
might need a non-obvious and somehow obscure adjustment of the form
%F A061494 a(n) = A061653( A042965( n+1 ))

Since A042965( 23 ) = 29 ; A042965( 24 ) = 31
and A061494( 21 ) = 8 ; A061494( 22 ) = 9
these 8,9 should be the values of A061653(n) at n=29 and n=31,
but they appear currently as
A061653( 28 ) = 8 ;  A061653( 30 ) = 9
This would indicate that the current offset should be increased by one,
i.e. current n'=1 should be n=2, as you say.

BUT, the value  A061494( 27 ) = 37
which should correspond to the index A042965( 27 ) = 35
and now appears as  A061653( 36 )
would then appear as A061653( 37 )
and not as A061653( 35 ).

OTOH, the value 3  now appears at A061653( 22 ) and would,
upon shifting the offset from 1-> 2, appear as A061653( 23 )
while according to (current) A061494 and A042965 it would correspond to n=20...

Maximilian