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Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) is the least m such that n and k differ modulo m.
2

%I #10 Jul 12 2024 10:16:50

%S 2,3,2,2,3,2,3,2,3,2,2,3,2,3,2,4,2,3,2,3,2,2,4,2,3,2,3,2,3,2,4,2,3,2,

%T 3,2,2,3,2,4,2,3,2,3,2,3,2,3,2,4,2,3,2,3,2,2,3,2,3,2,4,2,3,2,3,2,5,2,

%U 3,2,3,2,4,2,3,2,3,2,2,5,2,3,2,3,2,4,2,3,2,3,2

%N Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) is the least m such that n and k differ modulo m.

%F T(n, k) = A007978(n-k).

%e Triangle T(n, k) begins:

%e n n-th row

%e -- ----------------------------------

%e 1 2

%e 2 3, 2

%e 3 2, 3, 2

%e 4 3, 2, 3, 2

%e 5 2, 3, 2, 3, 2

%e 6 4, 2, 3, 2, 3, 2

%e 7 2, 4, 2, 3, 2, 3, 2

%e 8 3, 2, 4, 2, 3, 2, 3, 2

%e 9 2, 3, 2, 4, 2, 3, 2, 3, 2

%e 10 3, 2, 3, 2, 4, 2, 3, 2, 3, 2

%e 11 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2

%e 12 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2

%t T[n_,k_]:=Module[{m=2},While[Mod[n,m]==Mod[k,m], m++]; m]; Table[T[n,k],{n,13},{k,0,n-1}]//Flatten (* _Stefano Spezia_, Jul 12 2024 *)

%o (PARI) T(n, k) = { for (m = 2, oo, if ((n%m) != (k%m), return (m););); }

%Y Cf. A007978, A374381, A374383.

%K nonn,easy,tabl

%O 1,1

%A _Rémy Sigrist_, Jul 06 2024