[seqfan] A015919

Tomasz Ordowski tomaszordowski at gmail.com
Mon Apr 16 13:10:32 CEST 2018


Hello, see

http://oeis.org/A015919

Theorem: if n is a term, then so is 2^n-1.

Conjecture: if 2^n-1 is a term, then so is n.

How far can you check my conjecture?

Please reply.

Best regards,

Thomas

P.S. Generally:

Let B be the set of natural numbers n such that

         (b^n-1)/(b-1) == 1 (mod n)

with a fixed integer b > 1.

My Last Conjecture:

The number (b^k-1)/(b-1) belongs to the set B if and only if k belongs to
B.

Note: This can be extended to bases b < -1.
________________________
Steuerwald's theorem (1948): If k is a psp(b) and gcd(k,b-1)=1, then
(b^k-1)/(b-1) is a psp(b).
Here a composite k is a psp(b) if and only if b^k == b (mod k).



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