

A154672


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


6



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
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OFFSET

1,1


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



FORMULA



MATHEMATICA

lst={}; Do[If[PrimeQ[n1]&&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[n1]&&PrimeQ[n+1], s=(n/5)^(1/2); If[Floor[s]==s, AppendTo[lst, n]]], {n, 6, 10!, 6}]; lst


PROG

(PARI) forstep(k=0, 1e4, 6, isprime(k^2*5+1) & isprime(k^2*51) & print1(k^2*5, ", ")) \\ M. F. Hasler, Apr 11 2009


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



