A160518 List of pairs of twin primes of the form 2k^3 +- 1.

431, 433, 18521, 18523, 1940597, 1940599, 3455999, 3456001, 30876497, 30876499, 88723727, 88723729, 105468749, 105468751, 164625749, 164625751, 431999999, 432000001, 451733057, 451733059, 615093749, 615093751, 746495999, 746496001, 1039436927, 1039436929

Offset

1,1

Comments

k is always divisible by 3. For the 5 pairs listed, k = 6, 21, 99, 120 and 249 (see A151612).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

6^3 = 216; 216*2 = 432; both 431 and 433 are prime.

Maple

isA001359 := proc(n) RETURN(isprime(n) and isprime(n+2)) ; end: for n from 1 to 1000 do twon3 := 2*n^3 ; if isA001359(twon3-1) then printf("%d, %d, ", twon3-1, twon3+1) ; fi; od: # R. J. Mathar, May 29 2009

Mathematica

s = Select[54*Range[300]^3, And @@ PrimeQ[# + {-1, 1}] &]; Flatten @
Transpose @ {s - 1, s + 1} (* Amiram Eldar, Dec 28 2019 *)

Crossrefs

Cf. A151612.

Sequence in context: A230574 A208627 A176387 * A273807 A323047 A046018

Adjacent sequences: A160515 A160516 A160517 * A160519 A160520 A160521

Keyword

nonn

Author

Howard Berman (howard_berman(AT)hotmail.com), May 16 2009

Extensions

More terms from R. J. Mathar, May 29 2009

More terms from Amiram Eldar, Dec 28 2019

Status

approved