A123085 - OEIS

%I #19 Sep 05 2023 12:15:13

%S 7,37,67,97,127,157,107,137,167,197,227,257,359,389,419,449,479,509,

%T 541,571,601,631,661,691,2221,2251,2281,2311,2341,2371,6673,6703,6733,

%U 6763,6793,6823,7457,7487,7517,7547,7577,7607,10103,10133,10163,10193,10223,10253

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

%H Harvey P. Dale, <a href="/A123085/b123085.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 Table starts:

%e     7,  37,  67,  97, 127, 157;

%e   107, 137, 167, 197, 227, 257;

%e   359, 389, 419, 449, 479, 509;

%e   ...

%p 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 Select[#+{0,30,60,90,120,150}&/@Prime[Range[1500]],AllTrue[#,PrimeQ]&]//Flatten (* _Harvey P. Dale_, Sep 05 2023 *)

%Y Cf. A001097, A156204 (first column).

%K nonn,tabf

%O 1,1

%A _Miklos Kristof_, Sep 27 2006