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A376079 a(n) is the largest difference of adjacent elements in the sorted list of the Collatz trajectory elements of n.

%I A376079 #12 Aug 24 2025 11:53:52
%S A376079 1,6,2,8,6,12,4,12,6,12,4,20,12,54,8,14,12,30,6,32,12,54,8,18,14,1944,
%T A376079 12,36,54,1944,16,18,12,54,12,56,30,66,20,1944,22,48,8,68,54,1944,24,
%U A376079 38,18,78,14,80,1944,1944,12,24,30,66,54,54,1944,1944,32,48,12
%N A376079 a(n) is the largest difference of adjacent elements in the sorted list of the Collatz trajectory elements of n.
%C A376079 Trajectories end when they reach 1.
%H A376079 Markus Sigg, <a href="/A376079/b376079.txt">Table of n, a(n) for n = 2..10001</a>
%e A376079 The trajectory of 3 is (3,10,5,16,8,4,2,1), the sorted list of the trajectory elements is (1,2,3,4,5,8,10,16), the list of differences is (1,1,1,1,3,2,6) with maximum 6, so a(3) = 6.
%t A376079 Table[Max[Differences[Sort[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]]]],{n,2,70}] (* _Harvey P. Dale_, Aug 24 2025 *)
%o A376079 (PARI) a(n) = my(L = List([n])); while(n > 1, n = if(n % 2 == 0, n/2, 3*n + 1); listput(L, n)); listsort(L); vecmax(vector(#L - 1, i, L[i+1] - L[i]));
%Y A376079 Cf. A220237 (sorted trajectory), A008908, A025586.
%K A376079 nonn,changed
%O A376079 2,2
%A A376079 _Markus Sigg_, Sep 09 2024