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A136188
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Digital roots of the Fermat numbers in A000215(n).
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0
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| Eric Weisstein's World of Mathematics, Digital Root.
Eric Weisstein's World of Mathematics, Fermat Number.
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FORMULA
| a(n)=DR(A000215(n))=A010888(A000215(n))
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EXAMPLE
| 2^(2^3) + 1 = 257. This has digital root 5 and hence a(3) = 5.
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MATHEMATICA
| FermatNumber[n_]:=2^(2^n)+1; DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[ # ]&, n]; DigitalRoot/@(FermatNumber[ # ] &/@Range[0, 25])
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CROSSREFS
| Cf. A000215, A010888, A135928.
Sequence in context: A020864 A152304 A021902 * A073334 A021740 A172370
Adjacent sequences: A136185 A136186 A136187 * A136189 A136190 A136191
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KEYWORD
| easy,base,nonn
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AUTHOR
| Ant King (mathstutoring(AT)ntlworld.com), Dec 24 2007
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