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If n is square, replace it with sqrt(n).
4

%I #21 Jul 22 2024 10:14:43

%S 0,1,2,3,2,5,6,7,8,3,10,11,12,13,14,15,4,17,18,19,20,21,22,23,24,5,26,

%T 27,28,29,30,31,32,33,34,35,6,37,38,39,40,41,42,43,44,45,46,47,48,7,

%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,8,65,66,67,68,69,70,71,72,73,74

%N If n is square, replace it with sqrt(n).

%F Sum_{n>=1} (-1)^(n+1)/n = 2*log(2) - Pi^2/12 = A016627 - A072691. - _Amiram Eldar_, Jul 07 2024

%e Among the first five integers 0, 1, 2, 3, and 4 the squares are 0, 1, and 4. Thus the first five terms in the sequence are 0, 1, 2, 3, and 2.

%t Table[If[IntegerQ[Sqrt[n]],Sqrt[n],n],{n,0,100}] (* _Harvey P. Dale_, Jul 09 2017 *)

%o (PARI) g(n) = for(x=0,n,if(issquare(x),y=sqrt(x),y=x);print1(floor(y)","))

%o (PARI) for(n=0,74,print1(if(issquare(n,&m),m,n)", ")) \\ _Zak Seidov_, Feb 21 2013

%Y Cf. A016627, A072691, A097449.

%K nonn,easy

%O 0,3

%A _Cino Hilliard_, Aug 23 2004