A050411 Analog of 3x+1 function.

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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

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

Links

• K. S. Stolarsky, A prelude to the 3x+1 problem, J. Differ. Equations Appl. 4 (1998), no. 5, 451-461.

Crossrefs

Cf. A000201, A001950, A005248, A189663.

Formula

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

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