A053597 Let prime(i) = i-th prime (A000040), let d(i) = prime(i+1)-prime(i) (A001223); a(n) = number of distinct numbers among d(n), d(n+1), d(n+2), ... before first duplicate is encountered.

2, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 2, 3, 3, 3, 3, 2, 3, 4, 3, 2, 2, 2, 3, 2, 5, 4, 3, 2, 3, 2, 1, 2, 2, 1, 3, 2, 3, 2, 3, 2, 1, 3, 2, 3, 4, 3, 3, 2, 1, 1, 2, 3, 5, 4, 4, 4, 3, 2, 5, 5, 5, 4, 5, 4, 3, 2, 2, 1, 2, 3, 3, 2, 4, 3, 2, 2, 4, 3, 2, 3, 4, 3, 2, 4, 3, 3, 2, 2, 6, 5, 4, 5, 4, 3, 2, 2, 1, 2, 3, 2

Offset: 1

Author

N. J. A. Sloane, Jan 07 2003

Keywords

• easy
• nonn

Examples

			The d sequence starting at prime(7) = 17 is d(7) = 2, d(8) = 4, d(9) = 6, d(10) = 2, with three numbers before the first duplication, so a(7) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A078515 gives RECORDS transform of this sequence. See also A079007.

Programs

Maple

P:= [seq(ithprime(i),i=1..1000)]:
G:= P[2..-1]-P[1..-2]:
R:= Vector(990):
for i from 1 to 990 do
  for k from 1 while nops(convert(G[i..i+k-1],set))=k do od:
  R[i]:= k-1;
od:
convert(R,list);

Mathematica

f[n_] := Block[{k = 1}, While[p = Table[ Prime[i], {i, n, n + k}]; Length[ Union[ Drop[p, 1] - Drop[p, -1]]] == k, k++ ]; k - 1]; Table[ f[n], {n, 1, 105}]

Extensions

More terms from Robert G. Wilson v, Jan 07 2002