[seqfan] Re: On some constellations of primes

[Hans Havermann]

Vladimir Shevelev:

> Every sequence is the union of 1) idea, 2) calculations. 06.10 in  
> seqfan list I exactly formulated the idea of future sequence  
> A217671. Hans published his A217658, using my idea +his constraint  
> (see his message from 10.10), submitting it 10.10 in 50 minits  
> before my (which is yet unpublished), and on my request to  
> calleagues to extend A217671, he wrote (10.10), instead of a real  
> help in extension, that my sequence is "already verified  and  
> extended". I am sure that it is, at least, incorrect.

I submitted A217658 (for the record, 10 hours 44 minutes before  
Vladimir's A217671) because on October 9 Vladimir asked me directly:  
"I hope that you (or you and Zak) can submit this sequence." By "this  
sequence", Vladimir of course meant something differently constrained,  
but I never liked his particular constraints because it seemed to  
create confusion more than enlightenment, at least in my mind (but  
then, I'm an empiricist, not a mathematician). No matter.

A217658 is 13, 19, 3, 73, 523, 6581, 10753, 231643, 387679, 43103,  
255259, 55457, 28751773, 328934789, 278689963, 784284211, 4440915607,  
8340839629, 30651695947.

A217671 was submitted as 3, 3, 3, 73, 523, 6581, 10753 and has been  
expanded, in draft form, to 3, 3, 3, 73, 523, 6581, 10753, 43103,  
43103, 43103, 55457, 55457 by Vladimir (October 10), and an additional  
28751773 by John W. Layman (October 12). In this forum, Charles  
Greathouse passed on Carlos Rivera's 278689963 and Carlos himself gave  
us the subsequent 784284211 on October 14 (even after Maximilian  
Hasler had already pointed out that the former was already in my  
A217658).

A217658 implies of course that A217671 will be 3, 3, 3, 73, 523, 6581,  
10753, 43103, 43103, 43103, 55457, 55457, 28751773, 278689963,  
278689963, 784284211, 4440915607, 8340839629, 30651695947, ... simply  
by substituting the earlier larger terms by their monotonic  
counterparts. That's what I meant by suggesting that Vladimir's  
sequence should be considered "verified and extended".

I don't know why A217671 hasn't been approved. Perhaps it is  
superfluous to A217658.

Hans