[seqfan] Re: A103969 is wrong, maybe useless

[Richard Mathar]

Reading http://list.seqfan.eu/pipermail/seqfan/2010-March/003862.html
 
mh> I don't know well Mmca either, but I'm quite sure that A005941(63)=64 is wrong ;
mh> Probably there is one term missing somewhere before A005941(62) =?= 39
mh> (39 should be the correct value for A005941(63) according to A5940(39) = 63.)

Indeed. The correct values of A005491 are

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 17, 12, 33, 18, 11, 16, 65, 14, 129,
20, 19, 34, 257, 24, 13, 66, 15, 36, 513, 22, 1025, 32, 35, 130,
21, 28, 2049, 258, 67, 40, 4097, 38, 8193, 68, 23, 514, 16385, 48,
25, 26, 131, 132, 32769, 30, 37, 72, 259, 1026, 65537, 44, 131073, 2050,
39, 64, 69, 70,


explicitly n, a(n)

40, 40
41, 4097
42, 38
43, 8193
44, 68
45, 23
46, 514
47, 16385
48, 48
49, 25
50, 26
51, 131
52, 132
53, 32769
54, 30
55, 37
56, 72
57, 259
58, 1026
59, 65537
60, 44
61, 131073
62, 2050
63, 39
64, 64
65, 69
66, 70

so A005491(61)=131073 is currently missing.

The formula in A005940 is incorrect and
should say  f((n-1)/2,i,x*prime(i))), not
f((n+1)/2,i,x*prime(i))) .

f := proc(n,i,x)
        option remember ;
        if n = 0 then
                x;
        elif type(n,'even') then
                procname(n/2,i+1,x) ;
        else
                # note the error in the formula: (n-1)/2, not (n+1)/2
                procname((n-1)/2,i,x*ithprime(i)) ;
        end if;
end proc:
A005940 := proc(n)
        f(n-1,1,1) ;
end proc:

A005941 := proc(n)
        local k ;
        for k from 1 do
                if A005940(k) = n then
                        return k;
                end if;
        end do ;
end proc: