please expand

Tanya Khovanova tanyakh at
Sat Oct 13 05:29:01 CEST 2007

Dear Neil,

I agree with you in spirit about ugly and artificial sequences.  I'm
certainly guity of some, and "the usual suspects" are generating them
rapidly enough to dilute the really nice sequences, as we've often

This one, however, is more natural than its correct retitling by Bob indicates.

It is as natural (under diagonalization) as noting that semiprimes are
products of two primes, and that 4-almost primes are products in
several ways of a pair of semiprimes, and (ab)-almost primes are
products in several ways of an a-almost prime and b-almost prime.

It started with my emailing Bob on 7 Oct 07:

(n-th n-almost prime) * ((n+1)-th (n+1)-AlmostPrime)
= A101695(n)*A101695(n+1) = (2n-1)-AlmostPrime(k)
where k = 2, 5, 11, 17, 25, 30, 45, 67 which is a mysterious seq not in
OEIS, which I can't explain except in terms of A101695.

1AP(1)*2AP(2) = 2 * 6 = 12 = 3AP(2)
2AP(2)*3AP(3) = 6 * 18 = 108 = 5AP(5)
3AP(3)*4AP(4) = 18 * 40 = 720 = 7AP(11)
4AP(4)*5AP(5) = 40 * 108 = 4320 = 9AP(17)
5AP(5)*6AP(6) = 108 * 224 = 24192 = 11AP(25)
6AP(6)*7AP(7) = 224 * 480 = 107520 = 13AP(30)
7AP(7)*8AP(8) = 480 * 1296 = 622080 = 15AP(45)
8AP(8)*9AP(9) = 1296 * 2688 = 3483648 = 17AP(67)

I sometimes think of myself as the borderline between those who
generate fewer but nicer sequences, and those who generate many but
ugly ones. If the quality of my submission has creeping up from the
mud, it is due to the great mentoring by you personally and your
wonderful associate editors, especially Bob Wilson, Ray Chandler, Tony
Noe, and some others who I skip here in interests of brevity, and by
feeback from seqfans. My father, in his many decades of New York book
publishing, advised a man who was famous for rapidly writing many
books in under a week each.  "Fastest book in the East" read the
prolific gent's business card. My father gently cautioned by quoting
the motto of Boston publisher Little Brown:  "Fewer books, but

In any case, I thank you again for your kindness and tolerence, and
tremendous strength in running such a huge project for so long.  I say
again that you should get a MacArthur Fellowship, for OEIS on top of
your major contributions in coding, lattices, editing, and so much


Jonathan Vos Post

On 10/13/07, N. J. A. Sloane <njas at> wrote:
> Bob, Jonathan:
>   I received this and i will add it to the OEIS.
> %S A115057 2,5,11,17,25,30,45,67,74,82,95,111,141,177,193,208,211,223,257,277,288,
> %T A115057 353,431,453,481,509,528,540,563,619,672,700,725,745,804,857,905,1003,
> %U A115057 1077,1127,1199,1268,1281,1321,1354,1379,1423,1517,1607,1660,1714,1748
> %N A115057 The number of (2n+1)-almost primes less than or equal to (n-th n-almost prime) * ((n\
> +1)-th (n+1)-almostprime).
> But it is rather artificial, don't you agree?
> It seems to contribute to the dilution of the OEIS by large
> numbers of ugly sequences, always contributed by the same few people.
> It would be easy to send in millions of similar sequences.
> The criterion should be, not "Is this sequence in the OEIS?",
> but rather "Is this sequence interesting?"
> Please exercise some restraint (and good judgement)!
> Neil

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