Terminology question about "Congruent Products Under XOR" and similar sequences (for index entry).

[Antti Karttunen]

Cheers,

I would like to create an index entries for these two kinds of sequences:
(because I'm submitting a lot more of them soon...)

>
>
> %S A115767 
> 0,3,6,11,12,22,24,43,44,48,51,86,88,96,99,102,171,172,176,179,192,
> %T A115767 
> 195,198,203,204,342,344,352,355,358,384,387,390,395,396,406,408,683,
> %U A115767 
> 684,688,691,704,707,710,715,716,768,771,774,779,780,790,792,811,812
> %N A115767 Integers i such that 2*i XOR 5*i = 3*i.
>

> %S A115770 
> 0,7,14,15,28,30,31,56,60,62,63,112,120,124,126,127,224,240,248,252,
> %T A115770 
> 254,255,448,455,480,496,504,508,510,511,896,903,910,911,960,967,992,
> %U A115770 
> 1008,1016,1020,1022,1023,1792,1799,1806,1807,1820,1822,1823,1920
> %N A115770 Integers i such that 7*i = A048720bi(11,i).
> %C A115770 Here * stands for ordinary multiplication, and A048720 is 
> the carryless (GF(2)[X]) multiplication.
> %H A115770 <a 
> href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index 
> entries for sequences operating on GF(2)[X]-polynomials</a>
>

How should I refer to these kind of sequences?
Should the first be called "Congruent Products" or "Congruent product 
identities"
or "Sequences defined by Congruent Products under XOR" ?

Or are we stretching the term "congruent" here a bit?
How about "XOR-congruent multiplicative/product identities"?

and should the second kind be called say "Cross-domain multiplicative identities"
or "Cross-domain product identities" ?
(E.g. as the is an ordinary multiplication * (of ring N) used at the right side
and the carryless multiplication A048720 (which makes its most natural sense in the GF(2)[X] polynomial ring)
at the right side.)


Or something else?

Yours,

Antti Karttunen



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