A016084 a(n+1) = a(n) + its digital root.

5, 10, 11, 13, 17, 25, 32, 37, 38, 40, 44, 52, 59, 64, 65, 67, 71, 79, 86, 91, 92, 94, 98, 106, 113, 118, 119, 121, 125, 133, 140, 145, 146, 148, 152, 160, 167, 172, 173, 175, 179, 187, 194, 199, 200, 202, 206, 214, 221, 226, 227, 229, 233, 241, 248, 253, 254

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1).

Formula

G.f.: x*(5+2*x^4+6*x^3-4*x^2)/((x+1)*(x^2-x+1)*(x-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; corrected by R. J. Mathar, Sep 16 2009

a(n) = (18*n - 9 + (-1)^n)/4 + 3*A128834(n). - Christian Krause, Apr 12 2026

E.g.f.: (4 + (9*x - 4)*cosh(x) + 4*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) + (9*x - 5)*sinh(x))/2. - Stefano Spezia, Apr 12 2026

Mathematica

dr[n_]:=NestWhile[Total[IntegerDigits[#]]&, n, #>9&]; NestList[#+dr[#]&, 5, 60] (* or *) LinearRecurrence[{2, -1, -1, 2, -1}, {5, 10, 11, 13, 17}, 90] (* Harvey P. Dale, Aug 15 2017 *)

Crossrefs

Sequence in context: A242994 A070791 A173901 * A007618 A004748 A038030

Adjacent sequences: A016081 A016082 A016083 * A016085 A016086 A016087

Keyword

nonn,base,easy

Author

Robert G. Wilson v

Status

approved