This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A136188 #29 Feb 16 2025 08:33:07 %S A136188 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, %T A136188 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, %U A136188 8,5,8,5,8,5,8,5,8,5,8,5,8,5,8,5,8,5,8 %N A136188 Digital roots of the Fermat numbers in A000215(n). %C A136188 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. %C A136188 Decimal expansion of 71/198. - _Enrique Pérez Herrero_, Nov 13 2021 %H A136188 I. Izmirli, <a href="https://doi.org/10.4236/apm.2014.46039">On Some Properties of Digital Roots</a>, Advances in Pure Mathematics, Vol. 4 No. 6 (2014), Article ID:47285. %H A136188 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>. %H A136188 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>. %H A136188 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1). %F A136188 a(n) = A010888(A000215(n)). %e A136188 2^(2^3) + 1 = 257. This has digital root 5 and hence a(3) = 5. %t A136188 FermatNumber[n_]:=2^(2^n)+1;DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[ # ]&,n];DigitalRoot/@(FermatNumber[ # ] &/@Range[0,25]) %o A136188 (PARI) a(n)=if(n,if(n%2,5,8),3) \\ _Charles R Greathouse IV_, May 01 2016 %Y A136188 Cf. A000215, A010888, A135928. %Y A136188 Essentially the same as A010719. %K A136188 easy,base,nonn %O A136188 0,1 %A A136188 _Ant King_, Dec 24 2007