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

1,1

Comments

All terms are multiples of 12.

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001043, A074924, A213784, A213789.

Sequence in context: A183742 A252618 A231112 * A260205 A224604 A045027

Adjacent sequences: A213808 A213809 A213810 * A213812 A213813 A213814

Keyword

nonn

Author

Zak Seidov, Jun 20 2012

Status

approved