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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Subsequence of A213739.

Sequence in context: A213347 A075476 A298977 * A085409 A303916 A111464

Adjacent sequences: A213781 A213782 A213783 * A213785 A213786 A213787

Keyword

nonn,nice

Author

Zak Seidov, Jun 19 2012

Status

approved