A073636 - OEIS

%I #41 Dec 14 2023 05:09:13

%S 1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,

%T 8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,

%U 9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9,1,8,9

%N Period 3: repeat [1, 8, 9] ; Digital root of A000578(n) = n^3 for n >= 1.

%C a(n) is the decimal expansion of 70/37. [_Enrique Pérez Herrero_, Jul 28 2009]; corrected by _David A. Corneth_, Jun 30 2016

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F G.f.: x*(9*x^2+8*x+1)/(1-x^3). - _Ant King_, Apr 30 2013

%F From _Wesley Ivan Hurt_, Jun 30 2016: (Start)

%F a(n) = a(n-3) for n>3.

%F a(n) = 6 + 3*cos(2*n*Pi/3) - 7*sin(2*n*Pi/3)/sqrt(3). (End)

%p seq(op([1, 8, 9]), n=1..50); # _Wesley Ivan Hurt_, Jun 30 2016

%t n=3; su[x_] := Sum[IntegerDigits[x][[i]], {i, Length[IntegerDigits[x]]}]; Table[su[su[su[su[x^n]]]], {x, 100}]

%t NestWhile[Total[IntegerDigits[#]] &, #1, # > 9 &] & /@ (Range[87]^3) (* _Jayanta Basu_, Jul 03 2013 *)

%o (Magma) &cat [[1, 8, 9]^^30]; // _Wesley Ivan Hurt_, Jun 30 2016

%Y Cf. A000578, A004164, A010888, A021596. Digital roots of squares are in A056992.

%K nonn,base,easy

%O 1,2

%A _Zak Seidov_, Sep 01 2002

%E Decimal expansion fraction corrected by _Ant King_, Apr 30 2013

%E Edited: name specified, offset changed from 0 to 1 (according to name), adjusted formula and g.f. for offset 1, digital root link added. - _Wolfdieter Lang_, Jan 05 2015