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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 (list; graph; refs; listen; history; text; internal format)
 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 Chai Wah Wu, Table of n, a(n) for n = 1..223 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 Cf. A000215, A002586, A019434, A020639. Sequence in context: A168116 A086022 A125649 * A219548 A218723 A097736 Adjacent sequences:  A219546 A219547 A219548 * A219550 A219551 A219552 KEYWORD nonn,changed AUTHOR Jonathan Sondow, Nov 28 2012 STATUS approved

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Last modified October 18 07:35 EDT 2019. Contains 328146 sequences. (Running on oeis4.)