A251780 Digital root of A069778(n-1) = n^3 - n^2 + 1, n >= 1. Repeat(1, 6, 3, 7, 6, 6, 4, 6, 9).

1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9, 1, 6, 3, 7, 6, 6, 4, 6, 9

Offset: 1

Author

Peter M. Chema, Dec 08 2014

Keywords

• base
• nonn
• easy

Comments

Periodic with cycle of 9: {1, 6, 3, 7, 6, 6, 4, 6, 9}.

The decimal expansion of 54588823/333333333 = 0.repeat(163766469).

Examples

			For a(3) = 3 because 3^3 - 3^2 + 3  = 27 - 9 + 3 = 21 with digit sum 3 which is also the digital root of 21.
		

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. A069778, A251754, A010888, A056992, A073636.

Programs

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 6, 3, 7, 6, 6, 4, 6, 9},108] (* Ray Chandler, Jul 25 2016 *)

PARI

DR(n)=s=sumdigits(n);while(s>9,s=sumdigits(s));s
for(n=1,100,print1(DR(abs(n^2-n-n^3)),", ")) \\ Derek Orr, Dec 30 2014

Formula

a(n) = digital root of n^3 - n^2 + n.

Extensions

More terms from Derek Orr, Dec 30 2014

Edited: name changed; formula, comment and example rewritten; digital root link added. - Wolfdieter Lang, Jan 05 2015