A154774 -id:A154774 - cp's OEIS frontend

A154674 Averages of twin prime pairs k such that k*11 and k/11 are squares.

990000, 1940400, 2227500, 6187500, 35640000, 54212400, 57182400, 74933100, 159677100, 164745900, 167310000, 194040000, 289485900, 380318400, 424205100, 496742400, 664101900, 684773100, 902919600, 976100400, 982327500, 1007433900

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A154670, A154671, A154672, A154673, A154774.

lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*11)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,11!,6}];lst...and/or... lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/11)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,11!,6}];lst
Select[11*Range[10^4]^2, And @@ PrimeQ[# + {-1, 1}] &] (* Amiram Eldar, Dec 25 2019 *)

for(i=1,999, isprime(9900*i^2+1) && isprime(9900*i^2-1) && print1(9900*i^2",")) \\ M. F. Hasler, Jan 15 2009

a(n) = 9900*A154774(n)^2. - M. F. Hasler, Jan 15 2009

More terms from M. F. Hasler, Jan 15 2009

A154775 Numbers k such that 13(6k)^2 is the average of a twin prime pair.

Original entry on oeis.org

2, 4, 5, 42, 46, 49, 59, 82, 84, 100, 119, 128, 137, 182, 185, 187, 192, 233, 264, 301, 303, 340, 376, 390, 395, 422, 438, 446, 471, 472, 494, 518, 527, 570, 598, 609, 611, 633, 667, 688, 714, 716, 726, 728, 733, 744, 831, 837, 865, 875, 896, 926, 940, 948

Offset: 1

M. F. Hasler, Jan 15 2009

nonn

Inspired by Zak Seidov's post to the SeqFan list, cf. link: This yields A154675 as 468 a(n)^2. Indeed, if N/13 is a square, then N=13 k^2 and this can't be the average of a twin prime pair unless k=6m.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Zak Seidov, "A154676", Jan 15 2009

Cf. A014574, A037073, A154331, A154772, A154773, A154774, A154675.

okQ[n_]:=Module[{av=468n^2},PrimeQ[av-1]&&PrimeQ[av+1]]; Select[Range[1000],okQ] (* Harvey P. Dale, Jan 21 2011 *)

for(i=1,999, isprime(468*i^2+1) & isprime(468*i^2-1) & print1(i","))

a(n) = sqrt(A154675(n)/468).

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A154674 Averages of twin prime pairs k such that k*11 and k/11 are squares.

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A154775 Numbers k such that 13(6k)^2 is the average of a twin prime pair.

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cp's OEIS Frontend

A154674 Averages of twin prime pairs k such that k*11 and k/11 are squares.

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Keywords

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Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A154775 Numbers k such that 13*(6*k)^2 is the average of a twin prime pair.

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A154775 Numbers k such that 13(6k)^2 is the average of a twin prime pair.