cp's OEIS Frontend

A251754 Digital root of A027444(n) = n + n^2 + n^3, n>=1. Repeat(3, 5, 3, 3, 2, 6, 3, 8, 9).

%I A251754 #36 Feb 16 2025 08:33:24
%S A251754 3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,
%T A251754 8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,
%U A251754 6,3,8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,8,9,3,5,3,3,2,6,3,8,9,3
%N A251754 Digital root of A027444(n) = n + n^2 + n^3, n>=1. Repeat(3, 5, 3, 3, 2, 6, 3, 8, 9).
%C A251754 Periodic with cycle of length 9: {3, 5, 3, 3, 2, 6, 3, 8, 9}.
%C A251754 a(n) also arises from the decimal expansion of 117775463/333333333 = 0.repeat(353326389).
%H A251754 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>.
%H A251754 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A251754 a(n) = sum of digits of (n+n^2+n^3), reduced to digital root.
%F A251754 a(n) = A010888(A027444(n)), and sequence may start at n=0.
%F A251754 a(n) = A010888(A010888(n) + A056992(n) + A073636(n)).
%F A251754 G.f.: x*(9*x^8 + 8*x^7 + 3*x^6 + 6*x^5 + 2*x^4 + 3*x^3 + 3*x^2 + 5*x + 3)/(1 - x^9). - _Chai Wah Wu_, Jul 17 2016
%e A251754 For a(11) = 5 because 11+11^2+11^3 = 1463, and 1+4+6+3 = 14.  Result is 5, which is the digital root of 14.
%t A251754 PadRight[{}, 120, {3, 5, 3, 3, 2, 6, 3, 8, 9}] (* _Vincenzo Librandi_, Jul 18 2016 *)
%o A251754 (Magma) &cat [[3,5,3,3,2,6,3,8,9]^^10]; // _Vincenzo Librandi_, Jul 18 2016
%Y A251754 Cf. A027444, A010888, A056992, A073636.
%K A251754 base,nonn,easy
%O A251754 1,1
%A A251754 _Peter M. Chema_, Dec 07 2014
%E A251754 Edited: name specified, digital root link added, a comment rewritten and moved to formula section. - _Wolfdieter Lang_, Jan 05 2015