login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..86.

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.

Index entries for linear recurrences with constant coefficients, signature (0,1).

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

Cf. A000215, A010888, A135928.

Sequence in context: A020864 A152304 A021902 * A073334 A021740 A172370

Adjacent sequences:  A136185 A136186 A136187 * A136189 A136190 A136191

KEYWORD

easy,base,nonn

AUTHOR

Ant King, Dec 24 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 16:03 EST 2022. Contains 350479 sequences. (Running on oeis4.)