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Both n + 1 and n/2 + 1 are primes.
3

%I #6 Dec 13 2018 19:06:30

%S 2,4,12,36,60,72,156,192,276,312,396,420,456,540,612,660,672,732,756,

%T 876,996,1092,1152,1200,1212,1236,1320,1380,1452,1620,1656,1752,1872,

%U 1932,1992,2016,2136,2340,2472,2556,2592,2796,2856,2916,3060,3216,3252

%N Both n + 1 and n/2 + 1 are primes.

%F a(n) = A005383(n)-1. - _Robert Israel_, Dec 13 2018

%t Select[Range[5*10^3], PrimeQ[ # + 1] && PrimeQ[ #/2 + 1] &]

%Y Cf. A005383.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jan 18 2004