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%I #28 Oct 22 2019 21:22:33
%S 0,1,6,2,0,7,7,3,5,1,12,8,10,8,8,4,6,6,4,2,15,13,58,9,56,11,52,9,36,9,
%T 15,5,28,7,13,7,20,5,18,3,18,16,16,14,59,59,59,10,14,57,57,12,55,53,
%U 51,10,22,37,55,10,24,16,22,6,35,29,14,8,27,14,12,8,10,21,23,6,27,19
%N a(n) is the number of iterations needed to reach 1 or 5 starting at n and using the map k -> (k/2 if k is even, otherwise k + (smallest triangular number > k)). Set a(n) = -1 if the trajectory never reaches 1 or 5.
%C It is conjectured that this algorithm will always terminate at 1 or 5.
%C _Jim Nastos_ verified the conjecture for n <= 354999.
%C The conjecture holds for all n <= 10^9. - _Jon E. Schoenfield_, Oct 20 2019
%F For n = 11: 11+15=26; 26/2=13; 13+15=28; 28/2=14; 14/2=7; 7+10=17; 17+21=38; 38/2=19; 19+21=40; 40/2=20; 20/2=10; 10/2=5; taking 12 steps to reach 5, so a(11)=12.
%Y Cf. A006577, A326823.
%K nonn
%O 1,3
%A _Ali Sada_, Oct 20 2019
%E Edited by _Jon E. Schoenfield_ and _N. J. A. Sloane_, Oct 20 2019