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A053597
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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.
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3
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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