A136188 - OEIS

A136188

Digital roots of the Fermat numbers in A000215(n).

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

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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