A270651 Triangular array: T(n,k) = greatest m such that 2^m divides prime(n)^2 - prime(k)^2, where 3 <= k <= n.

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, 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, 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

Offset

3,1

Links

Clark Kimberling, Table of n, a(n) for n = 3..10000

Example

First 9 rows (n = 3 up to 11)::
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   5   3
3   3   4   3   3   5   3   4   3
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).

Mathematica

a[n_] := Table[IntegerExponent[Prime[n]^2 - Prime[m]^2, 2], {m, 2, n - 1}]
TableForm[Table[a[n], {n, 2, 16}]]
Flatten[Table[a[n], {n, 2, 16}]]

Crossrefs

Cf. A000040, A270649.

Sequence in context: A303701 A179845 A180217 * A222635 A222649 A222616

Adjacent sequences: A270648 A270649 A270650 * A270652 A270653 A270654

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Apr 26 2016

Status

approved