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Search: Posts Made By: Dr Sardonicus
Forum: Puzzles 2020-09-01, 12:24
Replies: 20
Views: 3,506
Posted By Dr Sardonicus
The number of terms in the sum for N-digit "ok"...

The number of terms in the sum for N-digit "ok" numbers in the problem at hand is 5*6N-1, proving the sum is positive for every N. The smallest possible n is (as you indicate) 3*10N-1.

Since for...
Forum: Puzzles 2020-08-31, 11:58
Replies: 20
Views: 3,506
Posted By Dr Sardonicus
Although periodicity goes out the window, and...

Although periodicity goes out the window, and again it can never lead to a proof, Benford's Law tells us that the proportion of n for which the block of k leading digits is lacking a given nonempty...
Forum: Puzzles 2020-08-30, 02:33
Replies: 20
Views: 3,506
Posted By Dr Sardonicus
FWIW, it appears that the last power of 2 that...

FWIW, it appears that the last power of 2 that does not contain all ten decimal digits is

2^168 = 374144419156711147060143317175368453031918731001856

which lacks the decimal digit 2.

Every...
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