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Old 2020-01-09, 11:56   #1
Mar 2018

52710 Posts
Default Congruent to 10^n mod 41

215, 51456, 69660, 92020 and 541456 are the k's such that pg(k) is prime and k is congruent to 10^n mod 41 for n some nonneg integer
I think it is surprising that in the case k is NOT a multiple of 3 (k=215, 92020, 541456)

Then (k-10^n)/41 is a number A such that inserting a 0 in each pair of adjacent digits it turns out to be a multiple of A.
Example (541456-10)/41=13206. Inserting a 0 in each pair of adiajent dig its you have 103020006 which is a multiple of 13206.
The thing doesn't work when k is a multiple of 3 as in the cases 69660 and 51456

Last fiddled with by enzocreti on 2020-01-09 at 12:09
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