A232537 - OEIS

%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