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A080151 Let m = Wonderful Demlo number A002477(n); a(n) = sum of digits of m. 8
1, 4, 9, 16, 25, 36, 49, 64, 81, 82, 85, 90, 97, 106, 117, 130, 145, 162, 163, 166, 171, 178, 187, 198, 211, 226, 243, 244, 247, 252, 259, 268, 279, 292, 307, 324, 325, 328, 333, 340, 349, 360, 373, 388, 405, 406, 409, 414, 421, 430, 441, 454, 469, 486, 487 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also a(n) = sqrt(A080150(n)).

Record values in A003132: a(n) = A003132(A051885(n)). [Reinhard Zumkeller, Jul 10 2011]

LINKS

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Demlo Number

FORMULA

a(n)=(9^2)*(n/9-{n/9}+{n/9}^2)=81*(floor(x/9)+{x/9}^2), where the symbol {x} means fractional part of x. [Enrique Pérez Herrero, Nov 22 2009]

Empirical g.f.: x*(17*x^8+15*x^7+13*x^6+11*x^5+9*x^4+7*x^3+5*x^2+3*x+1) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Mar 05 2014

MATHEMATICA

(* by direct counting *)

Repunit[n_] := (-1 + 10^n)/9; A080151[n_]:=Plus @@ IntegerDigits[Repunit[n]^2];

(* by the formula * )

A080151[n_] := (9^2)*(n/9 - FractionalPart[n/9] + FractionalPart[n/9]^2)

(* or alternatively *)

A080151[n_] := 81*(Floor[n/9]+ FractionalPart[n/9]^2) (* Enrique Pérez Herrero, Nov 22 2009 *)

PROG

(Haskell) a n=(div n 9)*81+(mod n 9)^2

          A080151=map a [1..] \\ Chernin Nadav, Mar 06 2014

(PARI) vector(100, n, (n\9)*81+(n%9)^2) \\ Colin Barker, Mar 05 2014

CROSSREFS

Cf. A080150, A002477, A080160, A080161, A080162.

Sequence in context: A290934 A048387 A035121 * A292679 A106545 A169920

Adjacent sequences:  A080148 A080149 A080150 * A080152 A080153 A080154

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein, Jan 31 2003

STATUS

approved

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Last modified January 21 19:08 EST 2019. Contains 319350 sequences. (Running on oeis4.)