A213789 -id:A213789 - cp's OEIS frontend

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

Zak Seidov, Jun 20 2012

nonn

All terms are multiples of 12.

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

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

Cf. A001043, A074924, A213784, A213789.

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 *)

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

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

A212430 Numbers n such that n and n^4 are sums of two twin primes.

Original entry on oeis.org

384, 840, 8676, 33300, 34980, 37044, 39984, 42024, 50604, 53760, 55056, 61680, 64380, 71064, 83520, 88176, 97644, 103740, 120204, 129840, 133896, 148764, 154524, 160416, 168120, 173064, 184800, 188880, 199056, 207984, 234744, 266640, 292116, 307044, 356184

Offset: 1

Zak Seidov, Jun 21 2012

nonn

All terms are multiples of 12.

			384=191+193, 384^3=147456=73727+73729.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001043, A074924, A213784, A213789, A213811.

Select[12 Range[30000],AllTrue[{#/2+1,#/2-1,#^4/2+1,#^4/2-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 01 2017 *)

isok(n) = !(n % 2) && isprime(n/2-1) && isprime(n/2+1) && isprime(n^4/2-1) && isprime(n^4/2+1); \\ Michel Marcus, Oct 19 2013

n/2 +/-1 and (n^4)/2 +/- 1 are primes.

cp's OEIS Frontend

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

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