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A078856 Initial term in sequence of four consecutive primes whose consecutive differences have d-pattern = [6, 4, 6]; short d-string notation for pattern = [646].

%I A078856 #27 Aug 18 2017 19:34:29
%S A078856 73,157,373,433,1543,2341,2383,3313,3607,4441,4993,5851,6037,6961,
%T A078856 7237,8731,9613,9733,10723,13093,14143,14731,16411,16921,17971,18787,
%U A078856 20107,21391,23011,23593,25111,25237,25447,27793,30103,30697,32353,32563
%N A078856 Initial term in sequence of four consecutive primes whose consecutive differences have d-pattern = [6, 4, 6]; short d-string notation for pattern = [646].
%H A078856 R. J. Mathar, <a href="/A078856/b078856.txt">Table of n, a(n) for n = 1..1000</a>
%F A078856 Primes p = p_(i) such that p_(i+1) = p + 6, p_(i+2) = p + 6 + 4, p_(i+3) = p + 6 + 4 + 6.
%e A078856 p=73, 73 + 6 = 79, 73 + 6 + 4 = 83, 73 + 6 + 4 + 6 = 89 are consecutive primes.
%p A078856 N:=10^4: # to get all terms <= N.
%p A078856 Primes:=select(isprime,[seq(i,i=3..N+16,2)]):
%p A078856 Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1],
%p A078856 Primes[t+3]-Primes[t+2]]=[6,4,6], [$1..nops(Primes)-3])]; # _Muniru A Asiru_, Aug 04 2017
%t A078856 Transpose[Select[Partition[Prime[Range[10000]],4,1],Differences[#]=={6,4,6}&]][[1]] (* _Harvey P. Dale_, Apr 22 2014 *)
%Y A078856 Subsequence of A078562.
%Y A078856 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 A078856 nonn
%O A078856 1,1
%A A078856 _Labos Elemer_, Dec 11 2002
%E A078856 Listed terms verified by _Ray Chandler_, Apr 20 2009
%E A078856 Name simplified by _Michel Marcus_, Aug 11 2017