announcement: new page for submitting CHANGES to an entry

N. J. A. Sloane njas at
Wed Sep 3 19:49:45 CEST 2008

The sequence on the web page is the number of distinct prime
divisors of these numbers, taken together.  Thus, for example,
we don't count 7 in 2*5^2-1 = 49 = 7^2, because we have
already counted 7 for 2*2^2-1 = 7.

Section 4 (ignoring the spurious 1's) shows exactly what is
being counted.

As I noted, the web site could have used some editing and a lot
more explanation.  But it should only take about 5 or 10 minutes
looking at it to determine what is going on.

If you see something like this, get different results based on
your interpretation, and privately decide that the site is worth-
less, that's fine.  But if you are going to publicly criticize it, you
should take the additional time to determine for sure exactly
what the author is doing.

Note, by the way, that this procedure finds exactly the odd
primes for which 2 is a square; that is, those congruent to
+/- 1 mod 8.  That is, p|2x^2-1 means 2x^2 = 1 (mod p),
or x^2 = 1/2 (mod p).  And 1/2 has a square root mod p iff
2 does.

Franklin T. Adams-Watters

-----Original Message-----
From: Artur <grafix at>

Dear Seqfans, 

I was write mathematica procedure follow Franklin sugestion that 
aren't number of primes but number of prime divisors for numbers of the
form 2x^2-1 and x<=10^n. 

My result is fllowing 

*10, 154, 1904, 21741, 238392* 

Mathematica codes: 

l = 0; p = 2; a = {}; Do[k = p x^2 - 1; m = Divisors[k];
Do[If[PrimeQ[m[[y]]], l = l + 1], {y, 1,
Length[m]}];If[N[Log[x]/Log[10]] == Round[N[Log[x]/Log[10]]], Print[l];
 AppendTo[a, l]], {x, 1, 100000}]; a 

Mayby on mentioned www is nothing wrong (as Franklin belive) but what
author was mean are difficult puzzle to deknotting. 

Best wishes 


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