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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.
3
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
1,1
LINKS
EXAMPLE
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.
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}]
CROSSREFS
A078515 gives RECORDS transform of this sequence. See also A079007.
Sequence in context: A129363 A308342 A303399 * A230197 A094570 A225638
KEYWORD
easy,nonn
AUTHOR
N. J. A. Sloane, Jan 07 2003
EXTENSIONS
More terms from Robert G. Wilson v, Jan 07 2002
STATUS
approved