OFFSET
0,3
COMMENTS
In 1747, Euler showed that any factor of a Fermat number A000215(n) is of the form k*2^(n+1) + 1. See Wells at p. 148.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987.
FORMULA
EXAMPLE
The array begins as:
1, 3, 5, 7, 9, 11, 13, ...
1, 5, 9, 13, 17, 21, 25, ...
1, 9, 17, 25, 33, 41, 49, ...
1, 17, 33, 49, 65, 81, 97, ...
1, 33, 65, 97, 129, 161, 193, ...
1, 65, 129, 193, 257, 321, 385, ...
1, 129, 257, 385, 513, 641, 769, ...
...
MATHEMATICA
A[n_, k_]:=k*2^(n+1)+1; Table[A[n-k, k], {n, 0, 10}, {k, 0, n}]//Flatten
CROSSREFS
KEYWORD
AUTHOR
Stefano Spezia, Sep 14 2024
STATUS
approved