|
%I #6 Jul 13 2024 07:45:34
%S 2,3,2,2,2,2,5,2,3,2,2,3,2,2,2,7,2,3,2,5,2,2,2,2,2,2,2,2,3,2,3,2,3,2,
%T 3,2,2,5,2,2,2,3,2,2,2,11,2,3,2,5,2,7,2,3,2,2,2,2,3,2,2,2,2,2,2,2,13,
%U 2,3,2,5,2,7,2,3,2,11,2,2,7,2,2,2,3,2,2,2,5,2,2,2
%N Triangle T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the least prime number p such that the p-adic valuations of n and k differ.
%F T(n, 1) = A020639(n).
%F T(n, n-1) = 2.
%F T(2^n, k) = 2.
%F T(p, k) = A020639(k) for any prime number p and k > 1.
%e Triangle T(n, k) begins:
%e n n-th row
%e -- -------------------------------
%e 2 2
%e 3 3, 2
%e 4 2, 2, 2
%e 5 5, 2, 3, 2
%e 6 2, 3, 2, 2, 2
%e 7 7, 2, 3, 2, 5, 2
%e 8 2, 2, 2, 2, 2, 2, 2
%e 9 3, 2, 3, 2, 3, 2, 3, 2
%e 10 2, 5, 2, 2, 2, 3, 2, 2, 2
%e 11 11, 2, 3, 2, 5, 2, 7, 2, 3, 2
%e 12 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2
%o (PARI) T(n, k) = { forprime (p = 2, oo, my (d = valuation(n, p) - valuation(k, p)); if (d, return (p););); }
%Y Cf. A020639, A374369.
%K nonn,easy,tabl,new
%O 2,1
%A _Rémy Sigrist_, Jul 08 2024
|
