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 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 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

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