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A372085 Primes starting a sequence of 6 consecutive primes with gaps 2, 4, 8, 16, 32.

%I A372085 #13 Apr 30 2024 06:09:05
%S A372085 6824897,10132607,12674657,13699457,14148047,27353237,43918997,
%T A372085 44152307,50608007,53944337,60426257,60825827,61325057,68721047,
%U A372085 68933717,72069707,78577817,82108127,82334297,87020177,88226777,97013927,102043757,106053917,122271557,140859707,146049047,161788787,162036227
%N A372085 Primes starting a sequence of 6 consecutive primes with gaps 2, 4, 8, 16, 32.
%C A372085 First differs from A079015 at a(25) = 122271557.
%C A372085 All terms == 7 (mod 10).
%H A372085 Robert Israel, <a href="/A372085/b372085.txt">Table of n, a(n) for n = 1..1000</a>
%H A372085 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%e A372085 a(3) = 12674657 is a term because 12674657 is prime and the next five primes are 12674657 + 2 = 12674659, 12674659 + 4 = 12674663, 12674663 + 8 = 12674671, 12674671 + 16 = 12674687 and 12674687 + 32 = 12674719.
%p A372085 p:= 2: state:= 1: count:= 0: Res:= NULL:
%p A372085 while count < 100 do
%p A372085   q:= nextprime(p);
%p A372085   if q - p = 2^state then
%p A372085      state:= state+1;
%p A372085      if state = 6 then
%p A372085        count:= count+1; Res:= Res,q-62;
%p A372085      fi;
%p A372085   else state:= 1
%p A372085   fi;
%p A372085   p:= q;
%p A372085 od:
%p A372085 Res;
%Y A372085 Cf. A079015, A372248 (gaps 2,4,8,16).
%K A372085 nonn
%O A372085 1,1
%A A372085 _Zak Seidov_ and _Robert Israel_, Apr 17 2024