A023153 through A023161

[David Wilson]

Tony Noe has found that A023153 through A023161 are not multiplicative as I 
had marked them.

At the time, I was convinced that in sequence {s_k(n) = k^(2^n)}, a cycle of 
period x (mod a) and a cycle of period y (mod b) implied a unique cycle of 
period xy (mod ab). However, if gcd(x, y) > 1, the cycles (mod a) and (mod 
b) can align in more than one way, producing more than one cycle (mod ab). 
For example, the cycle (2,4) (mod 7) and the cycle (4,7) (mod 9) produce two 
cycles (4,16) and (25,58) (mod 63). This means that sometimes f(ab) > 
f(a)f(b).

This problem affects A023153 through A023161, and Tony Noe has shown that 
indeed none of these are multiplicative.

NJAS: Please remove the "mult" keyword and any comments related to 
multiplicativity from A023153-A023161.

Tony: Since these sequences are almost multiplicative, but are not, and you 
seem to be investigating these sequences, could you please add lines such as

%C A023153 Not multiplicative: a(63) = 10, but a(7)*a(9) = 3*3 = 9.

Thanks for spotting my error, Tony. Seems I have been bitten by the dragon I 
released.

----- Original Message ----- 
From: "T. D. Noe" <noe at sspectra.com>
To: <davidwwilson at comcast.net>
Sent: Tuesday, November 14, 2006 2:06 AM
Subject: Question about A023161


> David, according to my calculations, this sequence fails to be
> multiplicative at a(667).
>
> Best regards,
>
> Tony
>
>
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