A154672 Numbers n = 5*k^2 such that n - 1 and n + 1 are (twin) primes (thus k=6*m).

180, 1620, 8820, 35280, 87120, 151380, 302580, 380880, 691920, 737280, 808020, 1393920, 5020020, 5767380, 7712820, 9604980, 10281780, 11160180, 12450420, 12736080, 14723280, 15138000, 17186580, 17860500, 18663120, 18779220, 19129680, 21300480

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Keywords

• nonn

Comments

Original definition: Averages of twin prime pairs n such that n*5 and n/5 are squares.

Obviously, n*5 is a square iff n/5 is a square, say k^2. But n=5k^2 can't be the average of a twin prime pair unless it's a multiple of 6, thus k=6m and n=5*36*m^2. - M. F. Hasler, Apr 11 2009

Links

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

Crossrefs

Cf. A000290, A014574, A154670, A154671, A154673, A154674, A154675, A154676.

Programs

Mathematica

lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*5)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst (*...and/or...*) lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/5)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst

PARI

forstep(k=0,1e4,6, isprime(k^2*5+1) & isprime(k^2*5-1) & print1(k^2*5,",")) \\ M. F. Hasler, Apr 11 2009

Formula

A154672 = 5*A000290 intersect A014574 = 180*A000290 intersect A014574. - M. F. Hasler, Apr 11 2009

Extensions

Edited and extended by M. F. Hasler, Apr 11 2009