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A370265
Rectangular array, read by antidiagonals: T(n,k) = greatest m such that 2^m divides prime(n+k+1)-prime(n+1).
0
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
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 17 2024
STATUS
approved