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%I #11 Jul 11 2015 09:26:02
%S 2,19,67,89,173,373,587,1423,2377,2749,2879,4027,4507,4673,5189,6899,
%T 7523,8623,9319,10289,12373,12647,13487,14947,15859,17117,18757,19777,
%U 20123,21179,24509,25673,27673,28909,29327,32779,34123,38317,39769,47969,52919,54623
%N Primes p of the form penta(n)-3, where penta(n) is the n-th pentagonal number.
%C The n-th pentagonal number is (3*n^2-n)/2 = n*(3*n-1)/2.
%H K. D. Bajpai, <a href="/A232537/b232537.txt">Table of n, a(n) for n = 1..8500</a>
%e a(2)= 19: n= 4: (3*n^2-n)/2-3= 19, which is prime.
%e a(6)= 373: n= 16: (3*n^2-n)/2-3= 373, which is prime.
%p KD:= proc() local a,b; a:= (3*n^2-n)/2; b:=a-3; if isprime(b) then RETURN (b): fi; end: seq(KD(), n=1..500);
%t Select[Table[(n(3n-1))/2-3,{n,2,200}],PrimeQ] (* _Harvey P. Dale_, Jul 11 2015 *)
%Y Cf. A000326 (pentagonal numbers), A000040 (primes).
%K nonn
%O 1,1
%A _K. D. Bajpai_, Nov 25 2013