Beyond the OEIS

OEIS stands for the Online Encyclopaedia of Integer Sequences and, in my study of the integers associated with my diurnal age, I've found it to be an invaluable resource. Any registered person can propose a new sequence and in my initial enthusiasm, I decided to do just that. However, I was met with a firm rebuff and accused of creating a vanity sequence based on my diurnal age. It became quickly apparent that the OEIS is zealously guarded by a small group of individuals who must be approached in a certain manner.

I registered again under a new name and approached the arbiters in a less open and more guarded manner and succeeded in having my future submissions approved. It still rankled that I had to adopt such an approach and for some time now I haven't bothered to make any further submissions. Just lately, it occurred to me that I could concoct my own sequences, store them on Google Docs and even make them shareable and discoverable by others with no approval from the OEIS required.

The OEIS is a great resource and Neil Sloane is to be congratulated on being the inspiration behind its inception but he is quite old now and the duty of care for his creation has passed on to younger people. Unfortunately, the clique who now control the OEIS has created an unwelcoming atmosphere that discourages submissions by new contributors. Given my own advanced age and consequent life experiences, I was quickly able to discern what approach was needed in order to get these little Napoleons on side. This is why I registered again under a new name.

Such accommodations shouldn't be necessary and many younger contributors would be put off after their first rebuff. It's probably time for a new database of sequences to be created. Legally, it shouldn't be possible to own a sequence of numbers and so anybody or any group should be able to extract whatever sequences they want and start afresh. So far the sequences that I've created are not currently in the OEIS and I developed them because the existing OEIS entries held no interest for me.

Here is the link to the Google document that I've created:

https://docs.google.com/document/d/1pFqKbLCbhNCZ6euoUavt5QucPHfLRdiicWH_OHBw1L4/edit?usp=sharing

I'm not suggesting that there's anything amazing about these sequences but they're just as meaningful as a lot of the rubbish sequences that clutter up the OEIS today. To get an idea of the flavour of what I've created, here is a link to my latest sequence. Follow the link to see all five of them. These are early days yet and I'm likely to modify the layout in the future but for now:

S005: Composite numbers for which the set of digits associated with their prime factors is equal to the set of digits associated with the numbers themselves.

This sequence is a subset of S001.  

The first member of this sequence is \(132 = 2^2 \times 3 \times 11\) with the set of digits associated with 132 being {1, 2, 3} and the set of digits associated with its prime factors of 2, 3 and 11 also being {1, 2, 3}. 

 

The second member of the sequence, 312, has digits that are a permutation of the first member and that thus form the same set {1, 2, 3}. \(132 = 2^3 \times 3 \times 13\) and so its prime factors are 2, 3 and 13 with the associated set of digits being {1, 2, 3}. 

 

An algorithm (permalink) to generate the members of the sequence in the range from 1 to 30,000 is: 

 

L=[]
lower,upper=1,30000
for n in [lower..upper]:
    if is_prime(n)==0:
        D=Set(n.digits())
        DS=D.subsets()
        P=prime_factors(n)

        PS=[]

        for p in P:

            PS+=p.digits()

            if Set(PS)== D:

                L.append(n)

print("There are",len(L),"eligible numbers in the range from",lower,"to",upper,":")

print("This constitutes",numerical_approx(len(L)/(upper-lower)*100,digits=3),"percent of the range")

print()

print(L)

There are 61 eligible numbers in the range from 1 to 30000 :

This constitutes 0.203 percent of the range.

[132, 312, 735, 1255, 1377, 1775, 1972, 3792, 4371, 4773, 5192, 6769, 7112, 7236, 7371, 7539, 9321, 11009, 11099, 11132, 11163, 11232, 11255, 11375, 11913, 12176, 12326, 12595, 12955, 13092, 13175, 13312, 13377, 13491, 13755, 14842, 15033, 15303, 15317, 15532, 16332, 17272, 17276, 17343, 17482, 17973, 17975, 19075, 19276, 20530, 21345, 21372, 22413, 22714, 23535, 24338, 25030, 25105, 27232, 27393, 27944]

ADDENDUM September 2nd 2021

It seems I'll never learn. I made the mistake of proposing another sequence to the OEIS, throwing myself at the mercy of the little Napoleons guard its gates. Admittedly I'd made a couple of errors and had fixed them but then somebody asked why I thought the sequence was interesting. Hmmm. I saw where it was going so I bailed out, never to return again. I've learned my lesson.