A076217 - OEIS

%I #30 May 10 2024 12:29:41

%S 1,3,3,7,2,8,1,9,9,19,8,20,7,21,6,22,5,23,4,24,3,25,2,26,1,27,27,55,

%T 26,56,25,57,24,58,23,59,22,60,21,61,20,62,19,63,18,64,17,65,16,66,15,

%U 67,14,68,13,69,12,70,11,71,10,72,9,73,8,74,7,75,6,76,5,77,4,78,3,79,2,80

%N a(1)=1, a(n) = a(n-1) + n * sign(n-a(n-1)).

%C a(n) = 1 correspond to n = A058481(m). - _Bill McEachen_, Aug 31 2023

%H Reinhard Zumkeller, <a href="/A076217/b076217.txt">Table of n, a(n) for n = 1..10000</a>

%F If 3^n>2*m>= 2*3^(n-1); a(3^n-2*m) = m; if 3^n>2*m+1>=2*3^(n-1)+1 a(3^n-2*m-1) = 3^n - m; special case of partial sum: sum(k=1, 3^n, a(k)) = (3/8)*(9^n-1) + (3^(n+1)-1)/2.

%F Conjecture: a(n) = -a(n-1)+a(n-2)+a(n-3) for n>5.  G.f.: -x*(27*x^28 +54*x^27 +27*x^26 +9*x^10 +18*x^9 +9*x^8 +3*x^4 +6*x^3 +5*x^2 +4*x +1) / ((x -1)*(x +1)^2). - _Colin Barker_, Feb 25 2013

%e a(2) = a(1)+sign(2-a(1))*2 = 1 + 2 = 3.

%t RecurrenceTable[{a[1]==1,a[n]==a[n-1]+n Sign[n-a[n-1]]},a[n],{n,80}] (* _Harvey P. Dale_, Jun 14 2011 *)

%o (Haskell)

%o a076217 n = a076217_list !! (n-1)

%o a076217_list = 1 : zipWith (+) a076217_list

%o    (zipWith (*) [2..] $ map a057427 $ zipWith (-) [2..] a076217_list)

%o -- _Reinhard Zumkeller_, Apr 21 2013

%o (PARI) alist(N) = my(r, t=0); vector(N, i, t=r=t+i*sign(i-t)); \\ _Ruud H.G. van Tol_, May 10 2024

%Y Cf. A005132.

%Y Cf. A057427, A058481.

%K nice,nonn,look

%O 1,2

%A _Benoit Cloitre_, Nov 03 2002