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
Offset: 1
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).
Programs
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Haskell
a n=(div n 9)*81+(mod n 9)^2 A080151=map a [1..] \\ Chernin Nadav, Mar 06 2014 -
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
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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 *)
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PARI
vector(100, n, (n\9)*81+(n%9)^2) \\ Colin Barker, Mar 05 2014
Formula
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
Comments