A214175 -id:A214175 - cp's OEIS frontend

A217718 Primes of the form x^3 + y^3 - 1, where x and y are primes.

53, 151, 467, 2539, 3527, 6983, 7109, 30133, 31121, 31247, 34703, 41957, 50777, 59581, 62819, 68947, 69263, 75041, 79631, 81703, 91673, 98711, 106019, 109297, 110681, 159013, 183329, 205721, 228311, 228383, 231893, 239147, 256031, 256771, 295901, 302959, 312929

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Mar 21 2013

nonn

A number is in this sequence if it is prime, and can be expressed as p1^3 + p2^3 - 1, where p1 and p2 are also prime.

There are 175 numbers in the sequence < 10^7: a(175) = 83^3 + 211^3 - 1 = 9965717.

			3527 is in the sequence, because 11^3 + 13^3 - 1 = 3527, and 11, 13, and 3527 are all prime.

Christian N. K. Anderson, Table of n, a(n) for n = 1..1890

Cf. A024670 (sum of two cubes).

Cf. A214175 (primes that are one more than the sum of two prime cubes).

mx = 25; Union[Select[Flatten[Table[Prime[a]^3 + Prime[b]^3 - 1, {a, mx}, {b, a, mx}]], # < Prime[mx]^3 && PrimeQ[#] &]] (* T. D. Noe, Mar 29 2013 *)

A309856 Primes of the form 2*p^3+1 where p is also prime.

Original entry on oeis.org

17, 251, 2663, 48779, 410759, 715823, 2450087, 6615899, 13935743, 15290747, 23394167, 38930219, 160125983, 219804479, 236741543, 1258845587, 1666475243, 2116179719, 2308641299, 3604970627, 3991233959, 4283401139, 6109873703, 8207369603, 8487319319, 9264815927

Offset: 1

R. J. Mathar, Aug 20 2019

nonn

All terms == 5 (mod 6).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A309857.

Subsequence of A214175 and of A201107.

f:= proc(n) if isprime(n) and isprime(2*n^3+1) then return 2*n^3+1 fi end proc:
map(f, [2,seq(i,i=5..10000,6)]);# Robert Israel, Aug 22 2019

pp = Join[{2}, Select[Range[5, 10000, 6], PrimeQ[#] && PrimeQ[2#^3 + 1]&]];
2 pp^3 + 1 (* Jean-François Alcover, Jul 31 2020 *)
Select[2*Prime[Range[300]]^3+1,PrimeQ] (* Harvey P. Dale, Dec 09 2024 *)

a(n) = 1+2*A309857(n)^3.

cp's OEIS Frontend

A217718 Primes of the form x^3 + y^3 - 1, where x and y are primes.

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