

A251780


Digital root of A069778(n1) = n^3  n^2 + 1, n >= 1. Repeat(1, 6, 3, 7, 6, 6, 4, 6, 9).


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Periodic with cycle of 9: {1, 6, 3, 7, 6, 6, 4, 6, 9}.
The decimal expansion of 54588823/333333333 = 0.repeat(163766469).


LINKS

Table of n, a(n) for n=1..108.
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).


FORMULA

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


EXAMPLE

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.


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 *)


PROG

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


CROSSREFS

Cf. A069778, A251754, A010888, A056992, A073636.
Sequence in context: A246730 A200239 A097676 * A249542 A125123 A133612
Adjacent sequences: A251777 A251778 A251779 * A251781 A251782 A251783


KEYWORD

base,nonn,easy


AUTHOR

Peter M. Chema, Dec 08 2014


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


STATUS

approved



