A080151 - OEIS

A080151

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

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

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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

a(9*n + k) = 81*n + k^2, with k in range 0 to 9. - Enrique Pérez Herrero, Nov 05 2022

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