|
|
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
|
|
|
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
|
|
|
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^2-n-n^3)), ", ")) \\ Derek Orr, Dec 30 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Edited: name changed; formula, comment and example rewritten; digital root link added. - Wolfdieter Lang, Jan 05 2015
|
|
STATUS
|
approved
|
|
|
|