A213784 Numbers k such that both k and k^2 are sums of a twin prime pair.

12, 84, 204, 456, 1140, 5424, 10044, 11004, 13656, 17940, 27804, 36576, 43296, 62784, 72024, 87576, 87780, 94116, 99336, 107184, 120204, 131460, 161496, 165516, 168636, 179640, 187116, 190464, 197820, 213324, 219696, 235080, 235620, 244404, 251796, 263556

Offset: 1

Author

Zak Seidov, Jun 19 2012

Keywords

• nonn
• nice

Comments

Or, k such that k/2 +- 1 and (k^2)/2 +- 1 are primes. Hence all k's are multiples of 12.

Examples

			12 = 5 + 7, 12^2 = 144 = 71 + 73.
		

Links

• Zak Seidov and Harvey P. Dale, Table of n, a(n) for n = 1..1000 (first 430 terms from Zak Seidov)

Crossrefs

Subsequence of A213739.

Programs

Mathematica

Reap[ Do[ If[ And @@ PrimeQ /@ {n/2-1, n/2+1, n^2/2-1, n^2/2+1}, Sow[n]], {n, 12, 263556, 12}]][[2, 1]] (* Jean-François Alcover, Jul 17 2012 *)
tppQ[n_]:=And@@PrimeQ[n/2+{1,-1}]&&And@@PrimeQ[n^2/2+{1,-1}]; Select[ Range[ 12,300000,12],tppQ] (* Harvey P. Dale, Dec 20 2012 *)
Select[12*Range[22000],AllTrue[Flatten[{#/2+{1,-1},#^2/2+{1,-1}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 07 2015 *)

PARI

is(n)=if(n%12, return(0)); isprime(n/2-1) && isprime(n/2+1) && isprime(n^2/2-1) && isprime(n^2/2+1) \\ Charles R Greathouse IV, Jul 31 2016