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%I #30 Mar 10 2024 00:23:56
%S 2,4,5,8,9,12,13,16,20,21,25,28,29,32,36,40,41,45,48,49,53,56,60,65,
%T 68,69,72,73,76,85,88,92,93,100,101,105,109,112,116,120,121,128,129,
%U 132,133,141,149,152,153,156,160,161,168,172,176,180,181,185,188,189
%N Numbers k such that floor((3*k - 1)/2) is prime.
%C Numbers k such that A001651(k) is prime.
%C This sequence is infinite because values of the form floor((3*k-1)/2) include all primes except 3.
%H Iain Fox, <a href="/A296058/b296058.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = floor((2*prime(n+1) + 2)/3).
%F a(n) = A004523(A000040(n+1) + 1).
%e Floor((3*4 - 1)/2) = 5 is prime, so 4 is a term.
%e Floor((3*5 - 1)/2) = 7 is prime, so 5 is a term.
%e Floor((3*6 - 1)/2) = 8 is not prime, so 6 is not a term.
%t Select[Range[200], PrimeQ@ Floor[(3 # - 1)/2] &] (* or *)
%t Array[Floor[2 (Prime[# + 1] + 1)/3] &, 60] (* _Michael De Vlieger_, Dec 09 2017 *)
%o (PARI) is(n) = isprime(floor((3*n-1)/2))
%o (PARI) a(n) = floor((2*prime(n+1) + 2)/3)
%o (PARI) lista(nn) = forprime(p=3, nn, print1(floor((2*p + 2)/3), ", "))
%Y Characteristic function: A296028.
%Y Cf. A000040, A001651.
%K nonn
%O 1,1
%A _Iain Fox_, Dec 03 2017