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A240169 Numbers n such that (6n)^3 is the sum of a twin prime pair. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 20:41 EST 2022. Contains 350455 sequences. (Running on oeis4.)