A270651 - OEIS

A270651

Triangular array: T(n,k) = greatest m such that 2^m divides prime(n)^2 - prime(k)^2, where 3 <= k <= n.

%I #5 Apr 29 2016 17:31:36

%S 4,3,3,4,5,3,5,4,3,4,3,3,4,3,3,5,4,3,4,6,3,3,3,5,3,3,4,3,6,4,3,4,5,3,

%T 5,3,3,3,4,3,3,5,3,4,3,4,6,3,5,4,3,4,3,4,3,3,3,5,3,3,4,3,7,3,4,3,4,5,

%U 3,6,4,3,4,3,4,3,5,3,3,3,4,3,3,7,3,4,3,5,3,4,3,4,5,3,7,4,3,4,3,4,3,5,3,6,3

%N Triangular array: T(n,k) = greatest m such that 2^m divides prime(n)^2 - prime(k)^2, where 3 <= k <= n.

%H Clark Kimberling, <a href="/A270651/b270651.txt">Table of n, a(n) for n = 3..10000</a>

%e First 9 rows (n = 3 up to 11)::

%e 4

%e 3 3

%e 4 5 3

%e 5 4 3 4

%e 3 3 4 3 3

%e 5 4 3 4 6 3

%e 3 3 5 3 3 4 3

%e 6 4 3 4 5 3 5 3

%e 3 3 4 3 3 5 3 4 3

%e For n = 5, the numbers p^2 - q^2 are 121 - 9 = 16*7, 121 - 25 = 32*3, 121 - 49 = 8*7, so that row 3 (for n = 5) is (4, 5, 3).

%t a[n_] := Table[IntegerExponent[Prime[n]^2 - Prime[m]^2, 2], {m, 2, n - 1}]

%t TableForm[Table[a[n], {n, 2, 16}]]

%t Flatten[Table[a[n], {n, 2, 16}]]

%Y Cf. A000040, A270649.

%K nonn,tabl,easy

%O 3,1

%A _Clark Kimberling_, Apr 26 2016