cp's OEIS Frontend

A224325 First of three consecutive primes in arithmetic progression with gap of 6n, and such that a(n) > a(n-1).

%I A224325 #27 Dec 25 2013 02:53:36
%S A224325 47,199,20183,40039,69593,255767,689467,3565931,6314393,9113263,
%T A224325 12012677,23346737,43607351,69266033,75138781,324237847,460475467,
%U A224325 652576321,742585183,747570079,807620651,2988119207,12447231761
%N A224325 First of three consecutive primes in arithmetic progression with gap of 6n, and such that a(n) > a(n-1).
%C A224325 Without the condition on monotonicity, this would be essentially the same as A052187, but there 255767 is followed by 247099, while monotonicity here gives 689467. Similarly, following a(9) = A052187(10) = 6314393 we have a(10) = 9113263, while A052187(11) = 4911251. The next term which is not matching is a(14) = 69266033 vs A052187(15) = 34346203. One may notice that the two terms differ approximately by a factor of 2.
%H A224325 Pierre CAMI, <a href="/A224325/b224325.txt">Table of n, a(n) for n = 1..23</a>
%e A224325 a(1) = A047948(1) = 47 is the least prime p(k) such that p(k+1) - p(k) = p(k+2) - p(k+1) = 6.
%e A224325 a(2) = A052188(1) = 199 is the least prime p(k) > 47 such that p(k+1) - p(k) = p(k+2) - p(k+1) = 12.
%e A224325 a(3) = A052189(1) = 20183 is the least prime p(k) > 199 such that p(k+1) - p(k) = p(k+2) - p(k+1) = 18.
%e A224325 a(4) = A052190(1) = 40039 is the least prime p(k) > 20183 such that p(k+1) - p(k) = p(k+2) - p(k+1) = 24.
%e A224325 a(5) = A052195(1) = 69593 is the least prime p(k) > 40039 such that p(k+1) - p(k) = p(k+2) - p(k+1) = 30.
%o A224325 (PARI) g=6;o=2;forprime(p=2,,o+g==(o=p)||next;nextprime(p+1)==p+g||next;print1(p-g",");g+=6)
%Y A224325 Cf. A224324 (gaps of 30n).
%K A224325 nonn
%O A224325 1,1
%A A224325 _M. F. Hasler_, Apr 03 2013