A079015 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}.

6824897, 10132607, 12674657, 13699457, 14148047, 27353237, 43918997, 44152307, 50608007, 53944337, 60426257, 60825827, 61325057, 68721047, 68933717, 72069707, 78577817, 82108127, 82334297, 87020177, 88226777, 97013927, 102043757, 106053917, 114412937, 122271557

Offset: 1

Author

Labos Elemer, Jan 22 2003

Keywords

• nonn

Examples

			prime(45277466) = 884909087 is followed by {2, 4, 8, 16, 32, 10, 50, ...} difference pattern.
prime(9312431) = 166392559 initiates {4, 8, 16, 32, 64, 14, 30, ...} difference pattern of consecutive primes.
		

Crossrefs

Cf. A079011, A079012, A079013, A079014.

Programs

Mathematica

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}]
(* or *)
prmsUpTo[k_] :=
 First /@ Select[Partition[Prime@ Range[PrimePi[k]], 6, 1],
   Differences @# == {2, 4, 8, 16, 32} &]; prmsUpTo[10^9] (* Mikk Heidemaa, Apr 26 2024 *)

Extensions

More terms from Jinyuan Wang, Feb 10 2021