A240169 Numbers n such that (6n)^3 is the sum of a twin prime pair.

1, 29, 65, 81, 99, 136, 165, 174, 176, 191, 200, 266, 295, 301, 319, 346, 351, 370, 400, 411, 431, 434, 436, 456, 491, 494, 526, 541, 599, 651, 676, 714, 746, 790, 924, 956, 991, 1011, 1131, 1161, 1194, 1259, 1274, 1280, 1304, 1374, 1550, 1641, 1644, 1649, 1714, 1715, 1739, 1804, 1811, 1814, 1830, 1879, 1941, 2000

Offset

1,2

Comments

No terms end with 2, 3, 7, 8. Minimal differences are 1; e,g., a(52) - a(51) = 1715 - 1714. There are no three consecutive terms with common difference 1.

Distribution of last digits for first 61000 terms: W(0..9) = (10190, 10162, 0, 0, 10178, 10222, 10027, 0, 0, 10221).

For "existing" digits distribution is rather uniform.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Formula

a(n) = (1/6)*A245591(n+1)^(1/3).

Example

m = 1: (6m)^3 = 216 = 107 + 109, m = 29: (6m)^3 = 5268024 = 2634011 + 2634013.

Maple

select(n -> isprime(108 * n^3 - 1) and isprime(108 * n^3 + 1), [$1..1000]); # Robert Israel, Aug 03 2014

Mathematica

Select[Range[1000], PrimeQ[216#^3/2 - 1] && PrimeQ[216#^3/2 + 1] &] (* Alonso del Arte, Aug 02 2014 *)

Prog

(PARI) N=2*10^3; for(k=1, N, p=216*k^3; if(isprime(p/2-1)&&isprime(1+p/2), print1(k, ", ")))

Crossrefs

Cf. A245591.

Sequence in context: A039516 A134547 A259636 * A044131 A044512 A211492

Adjacent sequences: A240166 A240167 A240168 * A240170 A240171 A240172

Keyword

nonn

Author

Zak Seidov, Aug 02 2014

Status

approved