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A080151 Let m = Wonderful Demlo number A002477(n); a(n) = sum of digits of m. 9
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

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Demlo Number

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).

FORMULA

a(n) = A007953(A002477(n)).

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

a(n) = (9^2)*(n/9 - {n/9} + {n/9}^2) = 81*(floor(n/9) + {n/9}^2), where the symbol {n} means fractional part of n. - 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

Empirical g.f. confirmed. - Robert Israel, Aug 05 2019

MAPLE

f := n -> 9*n - 81*frac(1/9*n) + 81*frac(1/9*n)^2:

map(f, [$1..100]); # Robert Israel, Aug 05 2019

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,easy

AUTHOR

Eric W. Weisstein, Jan 31 2003

STATUS

approved

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Last modified May 18 23:41 EDT 2021. Contains 344009 sequences. (Running on oeis4.)