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