cp's OEIS Frontend

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.

%I A053597 #11 Jan 04 2021 13:53:29
%S A053597 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,
%T A053597 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,
%U A053597 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
%N 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.
%H A053597 Robert Israel, <a href="/A053597/b053597.txt">Table of n, a(n) for n = 1..10000</a>
%e A053597 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.
%p A053597 P:= [seq(ithprime(i),i=1..1000)]:
%p A053597 G:= P[2..-1]-P[1..-2]:
%p A053597 R:= Vector(990):
%p A053597 for i from 1 to 990 do
%p A053597   for k from 1 while nops(convert(G[i..i+k-1],set))=k do od:
%p A053597   R[i]:= k-1;
%p A053597 od:
%p A053597 convert(R,list);
%t A053597 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}]
%Y A053597 A078515 gives RECORDS transform of this sequence. See also A079007.
%K A053597 easy,nonn
%O A053597 1,1
%A A053597 _N. J. A. Sloane_, Jan 07 2003
%E A053597 More terms from _Robert G. Wilson v_, Jan 07 2002