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 A249160 Smallest number of iterations k such that A068527^(k)(n)=A068527^(k+1)(n). 1
 1, 0, 2, 1, 2, 3, 1, 2, 1, 4, 3, 2, 3, 1, 2, 1, 3, 2, 4, 3, 2, 3, 1, 2, 1, 5, 2, 3, 2, 4, 3, 2, 3, 1, 2, 1, 3, 4, 5, 2, 3, 2, 4, 3, 2, 3, 1, 2, 1, 2, 4, 3, 4, 5, 2, 3, 2, 4, 3, 2, 3, 1, 2, 1, 2, 3, 2, 4, 3, 4, 5, 2, 3, 2, 4, 3, 2, 3, 1, 2, 1, 3, 4, 2, 3, 2, 4, 3, 4, 5, 2, 3, 2, 4, 3, 2, 3, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Given a number n, denote its distance from next perfect square >= n as R(n), sequence A068527. The function R(n) has two fixed points, 0 and 2, and for all n>=3, R(n)=0, there exists a k>=0 such that R^(k)(n)=R^(k+1)(n)=0 or 2. This sequence gives the number of iterations needed to reach the fixed point starting at n. This sequence is unbounded, but grows very slowly, reaching records of 1, 2, 3, 4, 6 etc at n=1, 3, 6, 10, 26, 170, 7226, etc. LINKS EXAMPLE R(10) = 6, R(6) = 3, R(3) = 1, R(1) = 0, R(0) = 0. Thus a(10) = 4. MAPLE A249160 := proc(n)     local k, prev, this;     prev := n ;     for k from 1 do         this := A068527(prev) ;         if this = prev then             return k-1;         end if;         prev := this ;     end do: end proc: seq(A249160(n), n=1..80) ; # R. J. Mathar, Nov 17 2014 MATHEMATICA r[n_]:=Ceiling[Sqrt[n]]^2-n; Table[Length[FixedPointList[r, n]]-2, {n, 1, 100}] PROG (PARI) r(n)=if(issquare(n), 0, (sqrtint(n)+1)^2-n); le(n)=b=0; while(n!=0&&n!=2, b=b+1; n=r(n)); return(b); range(n) = c=List(); for(a = 1, n, listput(c, a)); return(c); apply(le, range(100)) CROSSREFS Cf. A068527. Sequence in context: A082691 A280052 A183198 * A269970 A252230 A036043 Adjacent sequences:  A249157 A249158 A249159 * A249161 A249162 A249163 KEYWORD nonn,easy AUTHOR Valtteri Raiko, Oct 22 2014 STATUS approved

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)