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A219549
Smallest prime factor of 2^(8n) + 1.
1
257, 65537, 97, 641, 257, 193, 257, 274177, 97, 65537, 257, 641, 257, 449, 97, 59649589127497217, 257, 193, 257, 641, 97, 65537, 257, 769, 257, 65537, 97, 641, 257, 193, 257, 1238926361552897, 97, 5441, 257, 641, 257, 65537, 97, 274177, 257, 193, 257, 641, 97, 65537, 257, 59649589127497217, 257, 65537, 97, 641, 257, 193, 257, 274177, 97, 65537, 257, 641, 257, 5953
OFFSET
1,1
COMMENTS
The smallest prime factor of 2^(8n+k) + 1 does not depend on n if 0 < k < 8 (see Formula in A002586).
For references and links, see A002586.
LINKS
FORMULA
a(n) = A002586(8n) = A020639(2^(8n) + 1).
a(2^(k-3)) = A020639(A000215(k)) is the smallest prime factor of the k-th Fermat number 2^(2^k) + 1.
EXAMPLE
a(1) = 2^8 + 1 = 257 is the Fermat prime A019434(3).
a(2) = 2^16 + 1 = 65537 is the Fermat prime A019434(4).
MATHEMATICA
Table[FactorInteger[2^(8*n) + 1][[1, 1]], {n, 20}] (* T. D. Noe, Nov 29 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Nov 28 2012
STATUS
approved