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Forum: Puzzles

2020-09-01, 12:24

Replies: 20

Does there exist another power of 2, except 65536, that doesn't contain a power of two digit?

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

Does there exist another power of 2, except 65536, that doesn't contain a power of two digit?

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

Does there exist another power of 2, except 65536, that doesn't contain a power of two digit?

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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