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

Offset: 1

Author

Peter M. Chema, Dec 07 2014

Keywords

• base
• nonn
• easy

Comments

Periodic with cycle of length 9: {3, 5, 3, 3, 2, 6, 3, 8, 9}.

a(n) also arises from the decimal expansion of 117775463/333333333 = 0.repeat(353326389).

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Digital Root.
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A027444, A010888, A056992, A073636.

Programs

Magma

&cat [[3,5,3,3,2,6,3,8,9]^^10]; // Vincenzo Librandi, Jul 18 2016

Mathematica

PadRight[{}, 120, {3, 5, 3, 3, 2, 6, 3, 8, 9}] (* Vincenzo Librandi, Jul 18 2016 *)

Formula

a(n) = sum of digits of (n+n^2+n^3), reduced to digital root.

a(n) = A010888(A027444(n)), and sequence may start at n=0.

a(n) = A010888(A010888(n) + A056992(n) + A073636(n)).

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

Extensions

Edited: name specified, digital root link added, a comment rewritten and moved to formula section. - Wolfdieter Lang, Jan 05 2015