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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 Table of n, a(n) for n=1..100. 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) = 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 Cf. A027444, A010888, A056992, A073636. Sequence in context: A292570 A161670 A135514 * A225581 A275391 A092553 Adjacent sequences: A251751 A251752 A251753 * A251755 A251756 A251757 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.)