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A217655 Consider sets of 3 consecutive primes a such that c - a = 200. The sequence gives the values of b.

%I A217655 #13 Jul 17 2025 17:03:47
%S A217655 8917523,17051707,24662467,25173593,27001199,37757639,38089453,
%T A217655 42629173,44310817,67142137,67816601,76317653,80517691,82772143,
%U A217655 82843753,83929789,84980743,90007363,94905269,99099773,99524219,117813307,119401577,129163457,147426791,162159887
%N A217655 Consider sets of 3 consecutive primes a<b<c such that c - a = 200. The sequence gives the values of b.
%H A217655 Zak Seidov, <a href="/A217655/b217655.txt">Table of n, a(n) for n = 1..1000</a>
%H A217655 Zak Seidov, <a href="/A217655/a217655.txt">Table of n, a, b, c for n=1..1000</a>
%e A217655 a(1) = 8917523 because {8917463, 8917523, 8917663} is the first set of 3 consecutive primes a, b, c with c-a = 200.
%p A217655 a :=2 :
%p A217655 b := nextprime(a) :
%p A217655 c := nextprime(b) :
%p A217655 for i from 1 do
%p A217655     if c-a= 200 then
%p A217655         print(b);
%p A217655     end if;
%p A217655     a := b ;
%p A217655     b := c ;
%p A217655     c := nextprime(b) ;
%p A217655 end do:  # _R. J. Mathar_, Nov 07 2012
%t A217655 Select[Partition[Prime[Range[91*10^5]],3,1],#[[3]]-#[[1]]==200&][[;;,2]] (* _Harvey P. Dale_, Jul 17 2025 *)
%Y A217655 Cf. A166251, A217561, A217566, A217577, A217603.
%K A217655 nonn
%O A217655 1,1
%A A217655 _Zak Seidov_, Oct 09 2012