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A185121 Smallest prime factor of 10^(2^n) + 1. 3
11, 101, 73, 17, 353, 19841, 1265011073, 257, 10753, 1514497, 1856104284667693057, 106907803649, 458924033, 3635898263938497962802538435084289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

10^k+1 can only be prime if k is a power of 2. So far only known primes in this sequence are a(0)=11 and a(1)=101.

a(n)>=2^(n+1)+1; we have a(n)=2^(n+1)+1 for n=7 and n=15.

a(14) > 10^16. - Max Alekseyev, Jun 28 2013

From the Keller link a(15)-a(20) = 65537, 8257537, 175636481, 639631361, 70254593, 167772161. - Ray Chandler, Dec 27 2013

LINKS

Table of n, a(n) for n=0..13.

FactorDB, Factorizations of 10^(2^n)+1

Makoto Kamada, Factorizations of 100...001

Wilfrid Keller, Prime factors of generalized Fermat numbers Fm(10) and complete factoring status

EXAMPLE

Example: for n=2, a(2)=73 since 10^(2^2) = 10001 = 73 * 137.

MATHEMATICA

Table[With[{k = 2^n}, FactorInteger[10^k + 1]][[1, 1]], {n, 0, 13, 1}] (* Vincenzo Librandi, Jul 23 2013 *)

PROG

(PARI) a(n) = factor(10^(2^n)+1)[1, 1] \\ Michel Marcus, May 30 2013

CROSSREFS

Cf. A038371, A000533, A000215, A093179, A102050

Essentially the same as A102050. - Sean A. Irvine, Feb 17 2013

Sequence in context: A036929 A168586 A073053 * A133835 A292451 A292731

Adjacent sequences:  A185118 A185119 A185120 * A185122 A185123 A185124

KEYWORD

nonn,more,hard

AUTHOR

Sergio Pimentel, Jan 22 2012

STATUS

approved

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Last modified July 19 12:47 EDT 2018. Contains 312775 sequences. (Running on oeis4.)