Small challenge

[Valentin Albillo]

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Hi again, J-F,

Well, since alleged solutions have already been posted, here's mine. First of all, the function being evaluated is at its simplest y = x¹⁰. The ending digits (5,6,9,4,1,0,1,4,9,6,5,) which are the ending digits of consecutive squares, plus the ten zeros in 10000000000 are hinting enough at the correct expression.

Now, if using the HP-71B, executing this from the command line produces your values exactly (suppresion of irrelevant trailing zeros in the scientific format aside):

>FOR X=5 TO 24 @ X^5^2 @ NEXT X

Thanks for the nice nanochallenge and best regards.
V.