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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.)