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A038371
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Smallest prime factor of 10^n+1.
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3
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2, 11, 101, 7, 73, 11, 101, 11, 17, 7, 101, 11, 73, 11, 29, 7, 353, 11, 101, 11, 73, 7, 89, 11, 17, 11, 101, 7, 73, 11, 61, 11, 19841, 7, 101, 11, 73, 11, 101, 7, 17, 11, 29, 11, 73, 7, 101, 11, 97, 11, 101, 7, 73, 11, 101, 11, 17
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) >= 7 for all n>0 since 10^n + 1 is then not divisible by 2, 3 or 5.
If n is odd, a(n)<=11 since every (base 10) palindrome of even length is divisible by 11. - M. F. Hasler, Apr 04 2008
Record values are a({0,1,2,16,32,64,...}). - M. F. Hasler, Apr 04 2008
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REFERENCES
| Ehrhard Behrends, Five-Minute Mathematics, translated by David Kramer. American Mathematical Society (2008) p. 7
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LINKS
| M. F. Hasler, Table of n, a(n) for n=0,...,500.
M. Kamada, Factorizations of 100...001
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FORMULA
| a(n)=A020639(A000533(n)).
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EXAMPLE
| a(12) = 73 as 10^12+1 = 1000000000001 = 73*137*99990001.
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MATHEMATICA
| Table[FactorInteger[10^n + 1][[1, 1]], {n, 0, 49}] (* Alonso del Arte, Oct 21 2011 *)
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PROG
| (PARI) A038371(n)=factor(10^n+1)[1, 1] - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 04 2008
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CROSSREFS
| Cf. A001221, A003021, A038371, A057934, A062397, A102050, A119704.
Sequence in context: A056732 A157715 A001271 * A003021 A097463 A083394
Adjacent sequences: A038368 A038369 A038370 * A038372 A038373 A038374
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KEYWORD
| nonn
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AUTHOR
| Miklos SZABO (mike(AT)ludens.elte.hu)
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 12 2002
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