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

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

1,1

Comments

All terms are multiples of 12.

Links

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

Formula

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

Example

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

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

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

Sequence in context: A384082 A110296 A179664 * A134175 A233886 A256735

Adjacent sequences: A212427 A212428 A212429 * A212431 A212432 A212433

Keyword

nonn

Author

Zak Seidov, Jun 21 2012

Status

approved