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A251754 Digital root of A027444(n) = n + n^2 + n^3, n>=1. Repeat(3, 5, 3, 3, 2, 6, 3, 8, 9). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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).
LINKS
Eric Weisstein's World of Mathematics, Digital Root.
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
EXAMPLE
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.
MATHEMATICA
PadRight[{}, 120, {3, 5, 3, 3, 2, 6, 3, 8, 9}] (* Vincenzo Librandi, Jul 18 2016 *)
PROG
(Magma) &cat [[3, 5, 3, 3, 2, 6, 3, 8, 9]^^10]; // Vincenzo Librandi, Jul 18 2016
CROSSREFS
Sequence in context: A292570 A161670 A135514 * A225581 A275391 A092553
KEYWORD
base,nonn,easy
AUTHOR
Peter M. Chema, Dec 07 2014
EXTENSIONS
Edited: name specified, digital root link added, a comment rewritten and moved to formula section. - Wolfdieter Lang, Jan 05 2015
STATUS
approved

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Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)