A213811 Numbers k such that k and k^3 are sums of two twin primes.

1044, 1200, 2604, 2964, 4056, 4284, 4476, 7164, 7644, 9300, 9864, 10884, 14616, 15180, 20916, 24084, 40716, 51156, 55056, 65436, 66144, 70104, 74676, 92100, 99060, 104580, 105804, 163944, 164700, 165780, 209604, 218400, 219660, 222540, 226656, 257040, 281676

Offset: 1

Author

Zak Seidov, Jun 20 2012

Keywords

• nonn

Comments

All terms are multiples of 12.

Examples

			1044=521+523, 1044^3=1137893184=568946591+568946593.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A001043, A074924, A213784, A213789.

Programs

Mathematica

sttpQ[n_]:=Module[{x=(n-2)/2},AllTrue[{x,x+2},PrimeQ]]; Select[Range[ 12,300000,12],sttpQ[#]&&sttpQ[#^3]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 25 2017 *)

PARI

isok(n) = !(n % 2) && isprime(n/2-1) && isprime(n/2+1) && isprime(n^3/2-1) && isprime(n^3/2+1); \\ Michel Marcus, Oct 19 2013

Formula

k/2 +/-1 and also (k^3)/2 +/- 1 are twin primes.