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A053597 Let p(i) = i-th prime (A000040), let d(i) = p(i+1)-p(i) (A001223); a(n) = number of distinct numbers among d(n), d(n+1), d(n+2), ... before first duplicate is encountered. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

The d sequence starting at p(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.

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

Adjacent sequences:  A053594 A053595 A053596 * A053598 A053599 A053600

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane, Jan 07 2003

EXTENSIONS

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

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)