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A078848 Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[2,6,4]; short d-string notation of pattern = [264].

%I A078848 #24 Mar 08 2020 18:55:48
%S A078848 29,59,71,269,431,1289,2129,2339,2381,2789,4721,5519,5639,5849,6569,
%T A078848 6959,8999,10091,13679,14549,16649,16691,18119,19379,19751,21491,
%U A078848 25931,27689,27791,28619,31181,32369,32561,32831,36779,41609,43961,45119
%N A078848 Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[2,6,4]; short d-string notation of pattern = [264].
%C A078848 Subsequence of A049437. - _R. J. Mathar_, Feb 10 2013
%H A078848 R. J. Mathar, <a href="/A078848/b078848.txt">Table of n, a(n) for n = 1..1000</a>
%F A078848 Primes p=p(i) such that p(i+1)=p+2, p(i+2)=p+2+6, p(i+3)=p+2+6+4.
%e A078848 29, 29+2=31, 29+2+6=37, 29+2+6+4=41 are consecutive primes.
%t A078848 d = {2, 6, 4}; First /@ Select[Partition[Prime@ Range[10^4], Length@ d + 1, 1], Differences@ # == d &] (* _Michael De Vlieger_, May 02 2016 *)
%t A078848 Select[Partition[Prime[Range[4700]],4,1],Differences[#]=={2,6,4}&][[All,1]] (* _Harvey P. Dale_, Mar 08 2020 *)
%Y A078848 Cf. analogous prime quadruple sequences with various possible {2, 4, 6}-difference-patterns in brackets: A007530[242], A078847[246], A078848[264], A078849[266], A052378[424], A078850[426], A078851[462], A078852[466], A078853[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].
%K A078848 nonn
%O A078848 1,1
%A A078848 _Labos Elemer_, Dec 11 2002
%E A078848 Listed terms verified by _Ray Chandler_, Apr 20 2009
%E A078848 Typo in example corrected by _Michel Marcus_, Dec 28 2013