[seqfan] Re: ambiquity of name "Isolated prime"

[Vladimir Shevelev]

Dear Юрий,
 
There are many notions depended on  parameter(s). For example, residues modulo k. If to consider the union of them, then, following  you, one can say that all integers are "residues".  Analogously, in my opinion, there is no a sense to use  the notion "isolated primes", not fixing a value of the parameter "k".  It is much better simply to say about  "the union over k of the k-isolated primes". In this sense your sequence is rather interesting and, in my opinion, could be published in OEIS. 
 
Remark 1. In A166251, I indeed introduced "isolated primes". But in that time there was unknown a notion of  "k-isolated primes" which I introduced later (see my link in A166251, Section 10), understanding that "isolated primes"="2-isolated primes" (as, for example, log(x)=log_e(x)).
Remark 2. I am confused that you refer to A186426. Please, see  A217561, A217566, A217577.
 
Regards,
Vladimir


----- Original Message -----
From: юрий герасимов <2stepan at rambler.ru>
Date: Tuesday, October 23, 2012 2:32
Subject: [seqfan] ambiquity of name "Isolated prime"
To: seqfan at list.seqfan.eu

> 
> Dear SegFans,
> If 
> 1)  single (non-twin or isolated) primes A001710,
> 2)  isolated primes A166251 (k = 2),  
> then 
> 3) primes A186426 (k = 3) are isolated primes ? 
> 4) the only prime p such that k*a < p < k*b for some k > 1 
> :   5, 7, 23, 37, 47, 53, 79, 83, 89, 113, 127, 163, 
> 167, 211, 223, 257, 277, 293, 307, 317, 331, 337, 359, 383, 389, 
> 397, 409, 449, 457, 467, 479, 509, 541, 557, 563, 577, 593, 631, 
> 673, 683, 691, 701, 709, 719, 751, 761, 769, 797, 839, 863, 877, 
> 887, 907, 911, 919, 929, 937, 977, 991, 1087, 1129, 1181, 1201, 
> 1213, 1237, 1249, 1259, 1283, 1297, 1307, 1327, 1361, 1381, 
> 1399, 1409, 1459, 1471, 1499, 1511... (I can't find the sequence 
> in the OEIS) are isolated primes ? 
> Under what name and in what form (4 or largest k > 1 such that 
> ...) to offer for publication in the OEIS ?
> Tranks is advance, 
> JSG
> 
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 Shevelev Vladimir‎