VOOZH about

URL: https://oeis.org/A136188

⇱ A136188 - OEIS


login
A136188
Digital roots of the Fermat numbers in A000215(n).
0
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, 8, 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, 8, 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, 8, 5, 8, 5, 8, 5, 8, 5, 8
OFFSET
0,1
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.
Decimal expansion of 71/198. - Enrique Pérez Herrero, Nov 13 2021
LINKS
I. Izmirli, On Some Properties of Digital Roots, Advances in Pure Mathematics, Vol. 4 No. 6 (2014), Article ID:47285.
Eric Weisstein's World of Mathematics, Digital Root.
Eric Weisstein's World of Mathematics, Fermat Number.
FORMULA
a(n) = A010888(A000215(n)).
EXAMPLE
2^(2^3) + 1 = 257. This has digital root 5 and hence a(3) = 5.
MATHEMATICA
FermatNumber[n_]:=2^(2^n)+1; DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[ # ]&, n]; DigitalRoot/@(FermatNumber[ # ] &/@Range[0, 25])
PROG
(PARI) a(n)=if(n, if(n%2, 5, 8), 3) \\ Charles R Greathouse IV, May 01 2016
CROSSREFS
Essentially the same as A010719.
Sequence in context: A359286 A152304 A021902 * A073334 A375338 A368741
KEYWORD
easy,base,nonn
AUTHOR
Ant King, Dec 24 2007
STATUS
approved