A370265 Rectangular array, read by antidiagonals: T(n,k) = greatest m such that 2^m divides prime(n+k+1)-prime(n+1).

1, 2, 1, 3, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 4, 1, 2, 3, 1, 1, 2, 1, 4, 2, 1, 1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 3, 1, 1, 5, 1, 1, 3, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 5, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 3

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Example

Corner:
   1  2  3  1  1  4  2  1  2  1  1  3  2  1  3  1
   1  1  3  2  1  1  3  1  5  2  1  1  4  1  3  1
   2  1  1  2  4  1  3  1  1  2  3  1  2  1  2  6
   1  1  3  2  1  2  1  1  5  2  1  4  1  3  2  1
   2  1  1  4  1  3  2  1  1  3  1  4  1  1  2  1
   1  1  2  1  2  3  1  1  2  1  2  1  1  3  1  1
   2  1  2  1  1  3  2  1  3  1  4  2  1  2  6  1
   1  3  1  1  2  3  1  2  1  2  4  1  3  2  1  1
   1  3  2  1  1  3  1  5  1  1  2  1  1  2  2  3
   1  1  2  4  1  2  1  2  3  1  4  2  1  1  1  3
Row 1 gives the greatest exponent m such that 2^m divides these differences of primes: 5-3, 7-3, 11-3, 13-3, 17-3, 19-3, 23-3,...

Mathematica

p[n_, k_] := p[n, k] = Prime[n + k + 1] - Prime[n + 1];
w[n_, k_] := Last[Select[Range[15], IntegerQ[p[n, k]/2^#] &]];
Table[w[n, k], {n, 1, 20}, {k, 1, 30}]  (* array *)
Table[w[n - k + 1, k], {n, 13}, {k, n, 1, -1}] // Flatten  (* sequence *)

Crossrefs

Cf. A000040, A023572 (row 1).

Sequence in context: A059130 A094959 A162696 * A364447 A309978 A108103

Adjacent sequences: A370262 A370263 A370264 * A370266 A370267 A370268

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 17 2024

Status

approved