[seqfan] Re: Offset in A001223?
franktaw at netscape.net
franktaw at netscape.net
Wed Mar 31 23:40:27 CEST 2010
First, you should note that the definition in question is a quotation
from the last reference listed in the "Links" section. This definition
is far from universal; for example, the second link to The World of
Mathematics (http://mathworld.wolfram.com/PrimeDifferenceFunction.html)
defines d_n = p_{n+1} - p_n, which is consistent with this sequence.
Generally, the rule in the OEIS is, when there are two equally good
possible values for the offset of a sequence, prefer to use offset 1.
It would be good to add an explicit formula to this sequence;
specifically a(n) = prime(n+1) - prime(n). I have submitted this
addition.
Franklin T. Adams-Watters
P.S. When quoting offset values for a sequence, just quote the first
value. The second one is automatically computed.
-----Original Message-----
From: Christopher Gribble <chris.eveswell at virgin.net>
Seqfans,
In the comment section of A001223, "Difference between consecutive
primes",
d(p_{k}) is defined as p_{k} - p_{k-1}, so the first value of d(p_{k})
listed is d(p_{2}) = d(3) . If the sequence is denoted by a(n), as in
Remi
Eismann's comment, then according to the offset (1, 2), n = k-1.
Wouldn't
it make more sense for the values of n and k to be consistent by
setting the
offset to 2, 2?
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