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Search: id:A136188
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| 3, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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As 2^(2^n)+1=5 (mod 9) for odd values of n, and 2^(2^n)+1=8 (mod 9) for even values of n>0 , it follows that the digital roots of the Fermat numbers form a cyclic sequence, with the 5's corresponding to odd values of n and the 8's to even values of n.
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LINKS
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Eric Weisstein's World of Mathematics, Digital Root.
Eric Weisstein's World of Mathematics, Fermat Number.
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FORMULA
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a(n)=DR(A000215(n))=A010888(A000215(n))
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EXAMPLE
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The fourth Fermat number is F(3)=257. This has digital root 5, and hence a(3)=5
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MATHEMATICA
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FermatNumber[n_]:=2^(2^n)+1; DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[ # ]&, n]; DigitalRoot/@(FermatNumber[ # ] &/@Range[0, 25])
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CROSSREFS
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Cf. A000215, A010888, A135928.
Adjacent sequences: A136185 A136186 A136187 this_sequence A136189 A136190 A136191
Sequence in context: A021283 A020864 A021902 this_sequence A073334 A021740 A110641
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KEYWORD
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easy,base,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Dec 24 2007
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