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A375206 T(n,k) for n >= 2, k < n is the distance of n and k in the Collatz graph, where T(n,k) is a triangle read by rows.

%I A375206 #19 Oct 18 2024 14:36:48
%S A375206 1,7,6,2,1,5,5,4,2,3,8,7,1,6,3,16,15,11,14,11,12,3,2,4,1,2,5,13,19,18,
%T A375206 14,17,14,15,3,16,6,5,1,4,1,2,10,3,13,14,13,9,12,9,10,2,11,5,8,9,8,2,
%U A375206 7,4,1,13,6,16,3,11,9,8,4,7,4,5,7,6,10,3,5,6,17,16,12,15,12,13,1,14,2,11,3,14,8,17,16,12,15,12,13,17,14,20,11,15,14,10,18
%N A375206 T(n,k) for n >= 2, k < n is the distance of n and k in the Collatz graph, where T(n,k) is a triangle read by rows.
%C A375206 The restriction k < n is there to avoid the trivial values T(n,n) = 0. Consequently, the first term is T(2,1).
%H A375206 Markus Sigg, <a href="/A375206/b375206.txt">Table of n, a(n) for n = 2..10012</a> (rows 2..142, flattened)
%H A375206 Hugo Pfoertner, <a href="/A375206/a375206.gif">Animated 3-d view of rows 2..200</a>, view angle tilted by 15 degrees against the n-k plane, 2024.
%e A375206 The triangle begins
%e A375206   1,
%e A375206   7, 6,
%e A375206   2, 1, 5,
%e A375206   5, 4, 2, 3,
%e A375206   8, 7, 1, 6, 3,
%e A375206   ...
%o A375206 (PARI) C(n) = {
%o A375206     my(L = List([n]));
%o A375206     while(n > 1, n = if(n % 2 == 0, n/2, 3*n+1); listput(L, n));
%o A375206     L
%o A375206 };
%o A375206 a375206(n,k) = {
%o A375206     my(Cn = C(n), Ck = C(k));
%o A375206     for(i = 1, #Cn,
%o A375206         for(j = 1, #Ck,
%o A375206             if(Cn[i] == Ck[j], return(i+j-2))
%o A375206         )
%o A375206     )
%o A375206 };
%Y A375206 Cf. A006370, A008908, A070165.
%K A375206 tabl,nonn
%O A375206 2,2
%A A375206 _Markus Sigg_, Oct 16 2024