[seqfan] Re: Semiprimes n such that n divides Fibonacci number F(n-1).

Charles Greathouse charles.greathouse at case.edu
Fri Dec 10 15:36:29 CET 2010

I'm a big fan of the less keyword, but I agree with its removal here.

> k-almost primes (I believe that njas hates that terminology)

I don't myself like the term but don't have a good replacement.  What
other terms are used?  I've occasionally seen k-primes (which mirrors
the 'alternate' terms biprime, triprime, etc.).  Anything else?

Charles Greathouse
Case Western Reserve University

On Thu, Dec 9, 2010 at 4:37 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> I do not strictly agree nor disagree with N. J. A. Sloane when he
> published my A177086. Let me clarify from my side.
> One set of my seqs are made this way.  I see something more or less
> important about primes, typically from a "nice" seq, often one tossed
> from the foam of the webcam.
> I see that it is nice, but consider that primality may be overly
> specific, and wonder what happens if one relaxes that assumption.  If
> one views the original seq through a prime factorization lens, then
> the special case of exactly two prime factors, and otherwise the same
> definition, gives a semiprime analogue of the prime-related seq.  This
> is merely the k=2 case, the original being a k=1 case, of k-almost
> primes (I believe that njas hates that terminology). Sometimes there
> is a, to me, interesting pattern if I look at the array A[k,n] = n-th
> value of the analogue with k-almost primes. If so, I tend to submit
> the main diagonal, A[n,n].
> From long experience, and sober judgment, njas signals that this is
> not an illuminating path by designating the semiprime analogue as
> "less" interesting.
> As I say, I never dispute the judgment of njas. He has been
> beneficent, creating the collaborationware in which we splash and play
> and work, and the wiki reflects his subcreation faithfully.
> The even more general analogy is to weaken or tighten the constraints
> in any seq, and see what happens.  That is "reading with a pencil" or
> webcamming with an open window. If the seq is additive, explore
> multiplicative.  If the seq is base 10, see if anything happens in
> other bases.  If quadratic, try cubic.
> In general, explore a small Hamming distance from "nice" -- or move
> orthogonally to a supersequence of sequences.
> One may stumble on something beautiful, or just be spinning your wheels.
> Your mileage may vary.
> In any case, I love OEIS, njas, seqfans, and the many friends that I
> have made in this cosmos.
> Let N thousand flowers bloom, for some non-arbitrary N.
> [steps down from soap box]
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