[seqfan] Re: Need help with A242866

[Max Alekseyev]

The old definition is not that interesting since 2^(2^k) + 2 is semiprine
only for k=0 and k=1.
For k > 1, we have 2^(2^k) + 2 = 2 * 3 * m, where integer m > 1, and so
2^(2^k) + 2 has at least three prime factors.
So, under the old definition the sequence would be the semiprimes in
A000215 united with { 4, 6 }.

Regards,
Max



On Sat, Sep 2, 2023 at 3:00 PM Neil Sloane <njasloane at gmail.com> wrote:

> Harvey Dale points out that there is a problem with A242866
>
> The old definition was
> Semiprimes of the form 2^(2^k) + 1 or 2^(2^k) + 2 for some k >= 0. +30
> 0
> with terms
> 6, 10, 34, 514, 131074, 4294967297, 18446744073709551617,
> 340282366920938463463374607431768211457,
>
> 115792089237316195423570985008687907853269984665640564039457584007913129639937
> The definition does not explain 10.  So I have replaced the definition with
> the old comment, which is:
>
> Union of 2*A019434 and the semiprimes in A000215.
>
> Two things: can someone check if this new definition matches the terms? Can
> someone create a new sequence to match the old definition?
>
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