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%I #12 May 19 2024 12:02:51
%S 6824897,10132607,12674657,13699457,14148047,27353237,43918997,
%T 44152307,50608007,53944337,60426257,60825827,61325057,68721047,
%U 68933717,72069707,78577817,82108127,82334297,87020177,88226777,97013927,102043757,106053917,114412937,122271557
%N Primes introducing consecutive prime 6-tuple of primes or 5-tuple corresponding consecutive p-difference pattern as follows: {d, 2*d, 4*d, 8*d, 16*d}.
%e prime(45277466) = 884909087 is followed by {2, 4, 8, 16, 32, 10, 50, ...} difference pattern.
%e prime(9312431) = 166392559 initiates {4, 8, 16, 32, 64, 14, 30, ...} difference pattern of consecutive primes.
%t d[x_] := Prime[x+1]-Prime[x]; k=0; Do[s=d[n]; If[Equal[d[n+1], 2*s]&&Equal[d[n+2], 4*s]&&Equal[d[n+3], 8*s] &&Equal[d[n+4], 16*s], k=k+1; Print[{n, Prime[n]}]], {n, 1, 100000000}]
%t (* or *)
%t prmsUpTo[k_] :=
%t First /@ Select[Partition[Prime@ Range[PrimePi[k]], 6, 1],
%t Differences @# == {2, 4, 8, 16, 32} &]; prmsUpTo[10^9] (* _Mikk Heidemaa_, Apr 26 2024 *)
%Y Cf. A079011, A079012, A079013, A079014.
%K nonn
%O 1,1
%A _Labos Elemer_, Jan 22 2003
%E More terms from _Jinyuan Wang_, Feb 10 2021
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