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 A222407 Digital roots of tribonacci numbers A000073. 3
 0, 0, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1, 9, 9, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1, 9, 9, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1, 9, 9, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS From a(2) onwards, periodic with period length 39. The period sums to 216 and contains no 3s. When divided into three sets of 13, further patterns are revealed in connection with A100402 (see link below). - Peter M. Chema, Dec 21 2016 LINKS FORMULA a(n) = A010888(A000073(n)). - Michel Marcus, Dec 19 2016 From Chai Wah Wu, Jan 30 2018: (Start) a(n) = a(n-1) - a(n-3) + a(n-4) - a(n-6) + a(n-7) - a(n-9) + a(n-10) - a(n-12) + a(n-13) - a(n-15) + a(n-16) - a(n-18) + a(n-19) - a(n-21) + a(n-22) - a(n-24) + a(n-25) - a(n-27) + a(n-28) - a(n-30) + a(n-31) - a(n-33) + a(n-34) - a(n-36) + a(n-37) for n > 38. G.f.: (-9*x^38 + 8*x^36 - 16*x^35 - x^34 + 15*x^33 - 20*x^32 + 4*x^31 + 12*x^30 - 17*x^29 + 10*x^27 - 17*x^26 - 2*x^25 + 10*x^24 - 15*x^23 + 3*x^22 + 3*x^21 - 11*x^20 + 2*x^19 + 2*x^18 - 5*x^17 - 4*x^16 + x^15 - x^14 - 4*x^13 - 4*x^12 - x^11 + x^10 - 5*x^9 - 5*x^8 + 2*x^7 - 3*x^6 - 3*x^5 - x^4 - x^2)/(x^37 - x^36 + x^34 - x^33 + x^31 - x^30 + x^28 - x^27 + x^25 - x^24 + x^22 - x^21 + x^19 - x^18 + x^16 - x^15 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 + x^4 - x^3 + x - 1). (End) MAPLE f:=proc(n) option remember; if n <= 1 then 0; elif n=2 then 1; else f(n-3)+f(n-2)+f(n-1); fi; end; # A000073 P:=n->if n=0 then 0 else ((n-1) mod 9) + 1; fi; # A010888 [seq(P(f(n)), n=0..200)]; MATHEMATICA FixedPoint[Total@ IntegerDigits@ # &, #] & /@ CoefficientList[ Series[x^2/(1 - x - x^2 - x^3), {x, 0, 81}], x] (* Michael De Vlieger, Dec 22 2016 *) CROSSREFS Cf. A000073, A010888, A210456. Sequence in context: A198503 A129200 A074958 * A230724 A167280 A236629 Adjacent sequences:  A222404 A222405 A222406 * A222408 A222409 A222410 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 20 2013 STATUS approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)