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Analog of 3x+1 function.
1

%I #18 Aug 17 2021 02:39:55

%S 4,1,7,9,2,12,3,15,17,4,20,22,5,25,6,28,30,7,33,8,36,38,9,41,43,10,46,

%T 11,49,51,12,54,56,13,59,14,62,64,15,67,16,70,72,17,75,77,18,80,19,83,

%U 85,20,88,21,91,93,22,96,98,23,101,24,104,106,25,109,111,26,114,27,117,119,28,122,29,125

%N Analog of 3x+1 function.

%C Iterates diverge for all n except n>2 in A005248.

%H K. S. Stolarsky, <a href="https://doi.org/10.1080/10236199808808155">A prelude to the 3x+1 problem</a>, J. Differ. Equations Appl. 4 (1998), no. 5, 451-461.

%F f([phi n]) = [phi^2 n]+2; f([phi^2 n]) = n. phi = (1+sqrt(5))/2.

%F a(n) = ceiling(ceiling(n/phi) * phi^2) + 1 if n is in A000201, otherwise a(n) = ceiling(n/phi^2) = A189663(n+1). - _Sean A. Irvine_, Aug 15 2021

%Y Cf. A000201, A001950, A005248, A189663.

%K nonn

%O 1,1

%A _David W. Wilson_