A137473 - OEIS

A137473

Positive numbers k such that k^3 +- (k-1)^2 are primes.

3, 6, 7, 13, 21, 73, 75, 90, 91, 97, 106, 115, 157, 201, 208, 238, 291, 300, 315, 358, 385, 405, 420, 460, 505, 523, 540, 651, 658, 798, 810, 825, 927, 942, 1000, 1105, 1125, 1135, 1186, 1197, 1278, 1315, 1365, 1378, 1380, 1410, 1417, 1476, 1480, 1483, 1557

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

3^3 +- 2^2 -> (23, 31) (both primes);

7^3 +- 6^2 -> (307, 379) (both primes).

MATHEMATICA

Select[Range[900], PrimeQ[ #^3-(#-1)^2]&&PrimeQ[ #^3+(#-1)^2]&]

PROG

(Magma) [n: n in [0..500] | IsPrime(n^3-(n-1)^2)and IsPrime(n^3 +(n-1)^2)] // Vincenzo Librandi, Nov 24 2010