A254867 Numbers n such that prime(n) + n and prime(n) + n^2 are prime.

1, 2, 4, 22, 66, 96, 106, 144, 180, 222, 324, 378, 466, 492, 604, 742, 760, 778, 784, 960, 984, 990, 994, 1050, 1150, 1162, 1186, 1248, 1302, 1308, 1356, 1360, 1380, 1744, 1830, 1866, 1870, 1956, 2052, 2070, 2112, 2182, 2212, 2380, 2470, 2556, 2586, 2638, 2676, 2760, 2766

Offset

1,2

Links

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

Example

a(4) = 22 = A064402(6): prime(22) = 79, 79 + {22, 22^2} = {101, 563} both prime.

Maple

A254867:=n->`if`(isprime(ithprime(n)+n) and isprime(ithprime(n)+n^2), n, NULL): seq(A254867(n), n=1..10^4); # Wesley Ivan Hurt, Jan 16 2017

Mathematica

Select[Range[1000], PrimeQ[Prime[#] + #] && PrimeQ[Prime[#] + #^2] &] (* Alonso del Arte, Feb 09 2015 *)
Select[Range[3000], AllTrue[Prime[#]+{#, #^2}, PrimeQ]&] (* Harvey P. Dale, Jan 17 2023 *)

Crossrefs

Subsequence of A064402. Cf. A000040, A014688, A061067, A061068.

Sequence in context: A152120 A072355 A134246 * A305492 A220456 A071298

Adjacent sequences: A254864 A254865 A254866 * A254868 A254869 A254870

Keyword

nonn

Author

Zak Seidov, Feb 09 2015

Status

approved