# A076150

Brian L. Galebach briang at SEGmail.com
Fri Nov 1 15:53:45 CET 2002

```Doesn't appear to be nonsense.  Just doing "decades" meaning all but the
last digit are the same for each possible number in the set, just as in year
decades.  This is in contrast to any set of 10 consecutive numbers where the
second-last digit changes at some point.

Reminds me of an argument everyone always has about when the new millenium
starts.  Well technically, every year is the beginning of a new millenium,
but it's not as meaningful to us.

Brian

-----Original Message-----
From: Ralf Stephan [mailto:ralf at ark.in-berlin.de]
Sent: Friday, November 01, 2002 8:50 AM
To: seqfan at ext.jussieu.fr
Subject: A076150

Bonjour!

Regarding...

%I A076150
%S A076150 201,321,511,531,621,841,891,1071,1131,1261,1331,1411,1461
%N A076150 m such that the decade m through m+9 is devoid of primes.
%C A076150 Since a decade of consecutive numbers may contain up to 4
primes,mor
e precisely a prime quadruplet(p,p+2,p+6,p+8) within a decade k through
k+9,whe
re 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
conse
cutive
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.
%Y A076150 Cf. A007530.
%K A076150 more,nonn,new
%O A076150 1,1
%A A076150 Lekraj Beedassy (beedassylekraj at hotmail.com), Oct 31 2002

... the entry is either nonsense or mistaken. If the submitter had meant
"start of ten consecutive composites" the sequence should have been

115, 117, 201, 213, 295, 297, 319, 321, 469, 511, 525, 527, 529, 531,
621, 663, 775, 777, 799, 841, 843, 865, 867, 889, 891, 893, 895, 897,
955, 957, 999, 1071, 1073, 1075, 1077, 1131, 1133, 1135, 1137, 1139,
1141,

but then the description is, um, a bit twisted. OTOH, if he meant "start of
ten
consecutive composites, starting with n = 1 mod 10" then he missed eg 1141.
I'm willing to resubmit IFF there is interest.

Greets,
ralf

```