A080370 Number of distinct values among the differences prime(j)-prime(i), 1 <= i < j <= n.

0, 1, 3, 5, 8, 10, 13, 15, 18, 22, 24, 28, 31, 33, 36, 40, 44, 46, 50, 53, 55, 59, 62, 66, 70, 74, 76, 79, 81, 84, 90, 95, 99, 101, 106, 109, 113, 117, 120, 124, 128, 130, 135, 138, 141, 143, 149, 155, 159, 161, 165, 169, 171, 176, 180, 184, 188, 191, 195, 198, 200

Offset

1,3

Links

Table of n, a(n) for n=1..61.

Example

n=1: no differences arise; n=3: primes={2, 3, 5}, C[3, 2]=3, differences={3, 2, 1}, a(3)=3;
n=7: primes={2, 3, 5, 7, 11, 13, 17}, differences={15, 14, 12, 10, 6, 4, 11, 10, 8, 6, 2, 9, 8, 6, 4, 5, 4, 2, 3, 2, 1}, distinct terms ={15, 14, 12, 11, 10, 9, 8, 6, 5, 4, 3, 2, 1}, a(7)=13.

Mathematica

f[n_] := Length[ Union[ Flatten[ Table[ Prime[i] - Prime[j], {i, 2, n}, {j, i - 1}]] ]]; Table[ f[n], {n, 61}] (* Robert G. Wilson v, Jul 30 2004 *)

Crossrefs

Sequence in context: A029919 A094227 A085225 * A175540 A210241 A190498

Adjacent sequences: A080367 A080368 A080369 * A080371 A080372 A080373

Keyword

nonn

Author

Labos Elemer, Feb 26 2003

Status

approved