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%I #9 Oct 10 2019 04:02:06
%S 257,65537,97,641,257,193,257,274177,97,65537,257,641,257,449,97,
%T 59649589127497217,257,193,257,641,97,65537,257,769,257,65537,97,641,
%U 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
%N Smallest prime factor of 2^(8n) + 1.
%C The smallest prime factor of 2^(8n+k) + 1 does not depend on n if 0 < k < 8 (see Formula in A002586).
%C For references and links, see A002586.
%H Chai Wah Wu, <a href="/A219549/b219549.txt">Table of n, a(n) for n = 1..223</a>
%F a(n) = A002586(8n) = A020639(2^(8n) + 1).
%F a(2^(k-3)) = A020639(A000215(k)) is the smallest prime factor of the k-th Fermat number 2^(2^k) + 1.
%e a(1) = 2^8 + 1 = 257 is the Fermat prime A019434(3).
%e a(2) = 2^16 + 1 = 65537 is the Fermat prime A019434(4).
%t Table[FactorInteger[2^(8*n) + 1][[1, 1]], {n, 20}] (* _T. D. Noe_, Nov 29 2012 *)
%Y Cf. A000215, A002586, A019434, A020639.
%K nonn
%O 1,1
%A _Jonathan Sondow_, Nov 28 2012
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