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Little explorations with HP calculators (no Prime)
01-13-2019, 10:48 AM (This post was last modified: 01-13-2019 11:07 AM by pier4r.)
Post: #343
RE: Little explorations with HP calculators (no Prime)
Another little problem that may be solved with a calculator, although the idea is that you try before without.

we have the numbers:
1 2 3 4 5 6 7 8

and we multiply those adjacent to one another, getting:
1x2 2x3 3x4 etc...
2 6 12 20 30 42 56
notice that now we have 7 numbers, not 8.

then we continue in this way until we have only one number.
Is this number smaller than 10^80 ?

if possible use spoilers as usual

Code:





















for example at my first estimation I estimated the last number would 
have an upper bound of 128 digits. Because we have:
line 1 max 8.
line 2 max 56
line 3 max 2352
thus line 4, 8 digits
line 5, 16
line 6, 32
line 7, 64
line 8, 128

Theb I refined it utilizing all the numbers trying to estimate the upper bound of theresulting multiplication in digits.
line 1: all 1 digits,
line 2: nnumbers with 1 digit and 2 digits
line 3: numbers from 2 to 4 digits
line 4: numbers from 4 to 8 digits
line 5: numbers from 9 to 15 digits
...
line 8: 96 digits


with the sharp el 506w I got ~ 6.64 e77 . So far away from my estimates.
And it appears I may have made a mistake while inputting numbers on the 506w.

Wikis are great, Contribute :)
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RE: Little explorations with HP calculators (no Prime) - pier4r - 01-13-2019 10:48 AM



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