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

Jonathan Post jvospost3 at gmail.com
Thu Dec 9 22:37:14 CET 2010

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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