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A123085 Table read by rows: rows give successive prime sextets of form k, k+30, k+60, k+90, k+120, k+150.

%I A123085 #19 Sep 05 2023 12:15:13
%S A123085 7,37,67,97,127,157,107,137,167,197,227,257,359,389,419,449,479,509,
%T A123085 541,571,601,631,661,691,2221,2251,2281,2311,2341,2371,6673,6703,6733,
%U A123085 6763,6793,6823,7457,7487,7517,7547,7577,7607,10103,10133,10163,10193,10223,10253
%N A123085 Table read by rows: rows give successive prime sextets of form k, k+30, k+60, k+90, k+120, k+150.
%H A123085 Harvey P. Dale, <a href="/A123085/b123085.txt">Table of n, a(n) for n = 1..1000</a>
%H A123085 Krishna Alladi, <a href="http://www.thehindu.com/todays-paper/tp-national/major-progress-in-prime-number-theory/article3038278.ece">The Green-Tao theorem resolves an important special case of the Erdos-Turan conjecture</a>, The Hindu, December 25 2006.
%e A123085 Table starts:
%e A123085     7,  37,  67,  97, 127, 157;
%e A123085   107, 137, 167, 197, 227, 257;
%e A123085   359, 389, 419, 449, 479, 509;
%e A123085   ...
%p A123085 i:=1:for k from 1 to 30000 do if isprime(k) and isprime(k+30)and isprime(k+60) and isprime(k+90) and isprime(k+120)and isprime(k+150) then a[i]:=k: a[i+1]:=k+30:a[i+2]:=k+60:a[i+3]:=k+90:a[i+4]:=k+120:a[i+5]:=k+150:i:=i+6 fi od: seq(a[n],n=1..i-1);
%t A123085 Select[#+{0,30,60,90,120,150}&/@Prime[Range[1500]],AllTrue[#,PrimeQ]&]//Flatten (* _Harvey P. Dale_, Sep 05 2023 *)
%Y A123085 Cf. A001097, A156204 (first column).
%K A123085 nonn,tabf
%O A123085 1,1
%A A123085 _Miklos Kristof_, Sep 27 2006