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Wagstaff Number $2617$ can be expressed as $7^4+6^3$.

Is there an Oeis sequence that lists all the numbers that can be expressed as the sum of a Power of six and a Power of seven? Are there other Wagstaff numbers that can be expressed in such a way?

$43$ Is another Wagstaff Number that can be written as $7+6^2$.

$13$ Is surely another Wagstaff which can be expressed as $6+7$

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    $\begingroup$ To make this self-contained: "Wagstaff numbers [are] numbers $k$ such that $(2^k + 1)/3$ is prime." (according to OEIS) But why are you asking whether $2617$ is the only such Wagstaff number, when you also say that $43$ and $13$ are such numbers? $\endgroup$
    – Gerry Myerson
    Commented Aug 8, 2023 at 7:47
  • $\begingroup$ Also $7 = 7^0 + 6^1$ is Wagstaff. $\endgroup$
    – Robert Israel
    Commented Aug 8, 2023 at 18:24

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I am not sure to have understood your question properly. Of course we can easily create an unlimited sequence of entries of the form $a(n):=7^b+6^c$ if we take $b=2,3,4, \ldots$ and $c=2,3,4, \ldots$ (sorting them in ascending order).

Now, if you need to search a specific sequence on the OEIS, a good idea is to put its first entries into the searching bar (and that's all), as an example we can find in a couple of minutes A303376 if we generate by ourselves the first four entries of the sequence we are interested in. In this case, $1^6+1^7$, $2^6+1^7$, and so forth up to $2^6+2^7=192$. Then, we just need to put those entries in the search bar and we are done.

Wagstaff numbers that are already listed on the OEIS can be found here: Wagstaff numbers on the OEIS.

Hoping this could help you with your research.

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  • $\begingroup$ Did you mean to link to A000978 instead of a search? $\endgroup$
    – LSpice
    Commented Aug 8, 2023 at 4:53
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    $\begingroup$ A000978 is the main sequence, but since the question was not very clear to me, I decided to add some other related info (i.e., by providing that link which includes A361562, A361563, etc...). It all depends on what set of rules @Twiga is really looking for. $\endgroup$
    – Marco Ripà
    Commented Aug 8, 2023 at 15:31
  • $\begingroup$ A226819 if you allow powers with exponent $\ge 0$. $\endgroup$
    – Robert Israel
    Commented Aug 8, 2023 at 18:34

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