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A178044 Primes of the form k^3 - 13. 2
499, 2731, 26987, 46643, 124987, 405211, 636043, 941179, 1560883, 1727987, 2406091, 2985971, 5451763, 6434843, 8489651, 10360219, 11239411, 11852339, 13823987, 18821083, 19682987, 22906291, 37933043, 42874987, 49836019 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See references of A176722.

For nonnegative integers k, (-k)^3 - 13 = -(k^3 + 13).

Necessarily, k = 6*j or k = 6*j + 2 as 4^3 - 13 = 3 * 17.

Values of k corresponding to terms of this sequence: 8, 14, 30, 36, 50, 74, 86, 98, 116, 120, 134, 144, 176, 186, 204, 218, 224, 228, 240, 266, 270, 284, 336, 350, 368, 396, 434, 476, 498, 534, 560, 564, 606, 620, 674, 704, 716, 746, 750, 756, 758, 914, 918, 924, 954, 966, 968, 974, 980, 1010.

k = 756 = 2^2 * 3^3 * 7 is the first positive integer (necessarily k = 6*j) such that both k^3 - 13 and k^3 + 13 are primes: p = 432081203 = prime(i), i = 22952658, p + 2*13 = prime(i+1).

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..2000

EXAMPLE

8^3 - 13 = 499 = prime(95) = a(1);

14^3 - 13 = 2731 = prime(399) = a(2).

MAPLE

for k from 1 to 10^4 do if isprime(k^3-13) then print(k^3-13); fi; od; # Muniru A Asiru, Jan 21 2018

MATHEMATICA

Select[Range[3, 500]^3 - 13, PrimeQ] (* Michael De Vlieger, Jan 21 2018 *)

PROG

(MAGMA) [ a: n in [3..500] | IsPrime(a) where a is n^3-13 ] // Vincenzo Librandi, Nov 30 2010

(GAP) o := [];; for k in [1..10^4] do if IsPrime(k^3-13) then Add(o, k^3-13); fi; od; o; # Muniru A Asiru, Jan 21 2018

CROSSREFS

Cf. A000040, A176722.

Sequence in context: A106761 A243957 A259890 * A230004 A203735 A093945

Adjacent sequences:  A178041 A178042 A178043 * A178045 A178046 A178047

KEYWORD

nonn

AUTHOR

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 18 2010

EXTENSIONS

More terms from Vincenzo Librandi, Jun 03 2010

STATUS

approved

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Last modified January 28 05:01 EST 2021. Contains 340490 sequences. (Running on oeis4.)