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Let x,y be odd numbers and symbol "m<+>k" be defined as in A179382. Consider sequence x<+>y, x<+>(3*(x<+>y)), x<+>(x<+>(3*(x<+>y))), x<+>(3*(x<+>(x<+>(3*(x<+>y)))),... ; a(n) is the smallest period in case x=2*n-1,y=1.
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%I #7 Mar 13 2024 19:20:19

%S 1,2,3,1,4,8,2,4,8,4,2,2,1,4,12,4,2,26

%N Let x,y be odd numbers and symbol "m<+>k" be defined as in A179382. Consider sequence x<+>y, x<+>(3*(x<+>y)), x<+>(x<+>(3*(x<+>y))), x<+>(3*(x<+>(x<+>(3*(x<+>y)))),... ; a(n) is the smallest period in case x=2*n-1,y=1.

%C The name contains an unmatched parenthesis. - Editors, Mar 13 2024

%e Let n=6, 2*n-1=11. We have 11<+>1=3, 11<+>(3*3)=5, 11<+>5=1, 11<+>(3*1)=7, 11<+>7=9, 11<+>(3*9)=19, 11<+>19=15, 11<+>(3*15)=7, 11<+>7=9,... Thus we have eventually periodic sequence with the smallest period 4 (with elements 7,9,19,15). Thus a(6)=4.

%Y Cf. A179382, A179480, A179686.

%K nonn,uned

%O 2,2

%A _Vladimir Shevelev_, Jul 25 2010