Found this one in an article by Richard Guy on the Strong Law of Small Numbers... *K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.

Is it always true? Is even the next one true?

Just a quick note on the notation a(n) for alternating factorial. I would think something like +/- n! is much more intuitive.

Spoiler (of sorts)

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Neil Calkin @neil_calkin offers:

solutions for 3,4,5,6,7,8,10,15,19,41,59,61,105,160 no more small values.

It continues

`661, 2653, 3069, and probables (3943, 4053, 4998, 8275, 9158, 11164, 43592, 59961)`... but the sequence is finite, and all prime terms in alternating factorials must be less than p = 3612701,If you love factor challenges f(9) = 36614981, and f(11)=36614981 (maybe easier)

The prime values of the prime terms are

3- 5

4 19

5 101

6- 619

7- 4421 8- 35899 10- 3301819 15- 1226280710981 19 115578717622022981 41- 32656499591185747972776747396512425885838364422981 59-136372385605079432248118270297843987319730859689490659519593045108637838364422981

61-499395599150088488088828589263699706832570087241364247806476254829684637838364422981 105-1071195818389184106041377222623114315174404652995290026861977169467051355218307761044337430404771512503239158647256903838408052353602736923780521178553460637838364422981 160-468544077492065936712052044718939948687543330546977719976017418129955876663406131164377030450551575840099843957105136480237871017419158043635450756712088769133544426722033165168878328322819566779381528981882285541609256481166622331374702000809600061055686236758821446539362161635577019

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