A154676 - OEIS

%I #12 Mar 13 2019 23:40:43

%S 2317500,12047292,26163648,43250112,47347452,61704828,168228252,

%T 333720000,351755712,426127068,513127872,840143808,979638768,

%U 998790588,1089276912,1330434108,1357220700,1388809152,1694467008,1927570428,1986835392,2035992348,2136108348,2858437872,3070594800,3241626300,3903322608

%N Numbers n = 103*k^2 such that (n-1,n+1) is a twin prime pair (thus k = 6*m).

%C Original definition: Averages of twin prime pairs n such that n*103 and n/103 are squares.

%C All terms are of the form 3708*k^2. - _Zak Seidov_, Jan 15 2009

%C Obviously n*103 is a square iff n/103 is a square, say k^2. But n=103k^2 can't be the average of a twin prime pair unless it's a multiple of 6, thus k=6m and n=103*36*m^2. - _M. F. Hasler_, Apr 11 2009

%H Robert Israel, <a href="/A154676/b154676.txt">Table of n, a(n) for n = 1..10000</a>

%p select(t -> isprime(t+1) and isprime(t-1), [seq(3708*i^2, i=1..2000)]); # _Robert Israel_, Mar 13 2019

%t lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*103)^(1/2); If[Floor[s]==s,AppendTo[lst,n]]],{n,9!,2*11!,6}]; lst (*...and/or...*) lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/103)^(1/2); If[Floor[s]==s,AppendTo[lst,n]]],{n,9!,2*11!,6}]; lst

%o (PARI) forstep(k=0,1e4,6, isprime(k^2*103+1) & isprime(k^2*103-1) & print1(k^2*103,",")) \\ _M. F. Hasler_, Apr 11 2009

%Y Cf. A154670, A154671, A154672, A154673, A154674, A154675.

%K nonn,less

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 14 2009

%E Edited and extended by _M. F. Hasler_, Apr 11 2009