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A213784 Numbers k such that both k and k^2 are sums of a twin prime pair. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A111464 A004407

Adjacent sequences:  A213781 A213782 A213783 * A213785 A213786 A213787

KEYWORD

nonn,nice

AUTHOR

Zak Seidov, Jun 19 2012

STATUS

approved

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Last modified December 15 22:53 EST 2018. Contains 318157 sequences. (Running on oeis4.)