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A102050 a(n) = 1 if 10^(2^n)+1 is prime, otherwise smallest prime factor of 10^(2^n)+1. 2
1, 1, 73, 17, 353, 19841, 1265011073, 257, 10753, 1514497, 1856104284667693057, 106907803649, 458924033, 3635898263938497962802538435084289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

10^(2^14)+1 is composite, but no prime factors are known. The smallest known prime factors of 10^(2^15)+1 to 10^(2^18)+1 are 65537, 8257537, 175636481, 639631361. [Jeppe Stig Nielsen, Nov 04 2010]

LINKS

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

factordb.com, Status of 10^(2^n)+1.

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

FORMULA

If 10^(2^n)+1 is composite, a(n) = A185121(n).

EXAMPLE

10^(2^4)+1 = 10000000000000001 = 353*449*641*1409*69857, hence a(4) = 353.

MATHEMATICA

spf[n_]:=Module[{c=10^2^n+1}, If[PrimeQ[c], 1, FactorInteger[c][[1, 1]]]]; Array[spf, 15, 0] (* Harvey P. Dale, Apr 09 2019 *)

PROG

(PARI) for(k=0, 8, fac=factor(10^(2^k)+1); print1(if(matsize(fac)[1]==1, 1, fac[1, 1]), ", "))

CROSSREFS

Cf. A000533, A002275.

Sequence in context: A099191 A051325 A249276 * A057446 A033393 A153646

Adjacent sequences:  A102047 A102048 A102049 * A102051 A102052 A102053

KEYWORD

nonn,hard,more,changed

AUTHOR

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

EXTENSIONS

a(13) from the Keller link, added by Jeppe Stig Nielsen, Nov 04 2010

STATUS

approved

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Last modified August 17 11:06 EDT 2019. Contains 326057 sequences. (Running on oeis4.)