A079011
Least prime p introducing prime-difference pattern {d, 2*d}, where d = 2*n, i.e., {p, p+2*n, p+2*n+4*n} = {p, p+2*n, p+6*n} are consecutive primes.
Original entry on oeis.org
5, 397, 503, 1823, 1627, 8317, 5939, 94153, 69539, 83117, 444187, 177019, 428873, 1179649, 955511, 1625027, 2541289, 1290683, 19856363, 12183757, 5412091, 23374859, 27248701, 38235013, 21369059, 34718041, 84120737, 59859131, 125283913, 44155159, 70136597, 324954127
Offset: 1
For n=3, d = 2*n = 6, d-pattern = {6, 12}, a(3) = 503, first corresponding prime triple is {503, 509, 521}.
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d[x_] := Prime[x+1]-Prime[x]; t=Table[0, {70}]; Do[s=d[n]/2; If[(d[n+1]==4*s)&&(t[[s]]==0), t[[s]]=Prime[n]], {n, 2, 100000}]; t
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a(n) = my(p=5, q=3, r=2); until(r+2*n==q&&q+4*n==p, r=q; q=p; p=nextprime(p+1)); r; \\ Jinyuan Wang, Feb 10 2021
Terms corrected and more terms from
Jinyuan Wang, Feb 10 2021
A079013
Least prime p introducing prime-difference pattern {d, 2*d, 4*d, 8*d}, where d = 2*n, i.e., {p, p+2*n, p+6*n, p+14*n, p+30*n} are consecutive primes.
Original entry on oeis.org
2237, 1197739, 8052641, 18365693, 151738897, 196061237, 946120169, 15367934161, 36116700523, 49526343773
Offset: 1
For n=4, d = 2*n = 8, d-pattern = {8, 16, 32, 64}, a(6)=18365693, first corresponding prime 5-tuplet is {18365693, 18365701, 18365717, 18365729, 18365793}.
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}.
Original entry on oeis.org
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
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.
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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 *)
A079014
a(n) is the least prime initiating consecutive prime difference pattern consisting of n increasing consecutive powers of 2 started with 2.
Original entry on oeis.org
2, 3, 5, 1997, 2237, 6824897, 1356705137, 3637803390827
Offset: 0
n=6: a(6) = p(67928439) = 1356705137 because {p, p+2, p+2+4, p+2+4+8, p+2+...+16, p+2+...+32, p+2+...+64} = {p, p+2, p+6, p+14, p+30, p+62, p+126} are consecutive primes.
Showing 1-4 of 4 results.