A076150

[Robert G. Wilson v]

Et al,

        I still do not like it. The "revised" edition begins with 115 which
implies that the numbers 115 through 124 are all composite. This is 
correct but
it is not the first.  The first six primes greater than 100 are 101, 
103, 107,
109, 113 & 127. I find that 114 - 123 are all composite. So are 116 - 
125 and
117 - 126.

        Therefore I believe that the sequence should be:
       
%S A076150 
114,115,116,117,200,201,212,213,294,295,296,297,318,319,320,321,468,
%T A076150 
469,510,511,524,525,526,527,528,529,530,531,620,621,662,663,774,775,
%U A076150 
776,777,798,799,840,841,842,843,864,865,866,867,888,889,890,891,892
%N A076150 Start of 10 consecutive composite numbers.
%C A076150 Since a decade of consecutive numbers may contain up to 4 
primes, more precisely a prime quadruplet(p, p+2, p+6, p+8) within a 
decade k through k+9, where k=p-1 or p(=A007530)excepting the first case 
(2, 3, 5, 7), this sequence may be regarded as a counterpart to A007530.
%e A076150 531 is in the sequence because it is the first term of the 
ten consecutive composites: 531=3^2*59; 532=2^2*7*19; 533=13*41; 
534=2*3*89; 535=5*107; 536=2^3*67; 537=3*179; 538=2*269; 539=7^2*11; 
540=2^2*3^3*5.
%t A076150 Select[ Range[900], Union[ Table[ PrimeQ[i], {i, #, # + 9}]] 
== {False} &]
%Y A076150 Cf. A007530, A076192.
%K A076150 nonn,new
%O A076150 1,1
%A A076150 Lekraj Beedassy (beedassylekraj at hotmail.com), Oct 31 2002
%E A076150 Corrected and extended by Ralf Stephan 
(ralf at ark.in-berlin.de), Nov 01, 2002



Ralf Stephan wrote:

>'The original submitter' asked me to edit the entry, so I'll do so.
>ralf
>
>----- Forwarded message from Lekraj Beedassy <boodhiman at yahoo.com> -----
>
>X-Sieve: cmu-sieve 1.3
>From: Lekraj Beedassy <boodhiman at yahoo.com>
>Subject: Re: A076150
>To: ralf at ark.in-berlin.de
>
>
>Hi Ralf,
>Actually, you're absolutely right all through. Submittal is certainly flawed since taken directly from a publication and consequently unverified.
>The proposed sequence's definition is indeed meant to be "start of ten prime-free consecutive numbers".
>Would you mind editing this sequence as notified?
>Thanx in advance,
>Lekraj Beedassy
> Ralf Stephan <ralf at ark.in-berlin.de> wrote:Bonjour!
>
>...
>%A A076150 Lekraj Beedassy (beedassylekraj at hotmail.com), Oct 31 2002
>
>----- End forwarded message -----
>
>  
>