A232537 Primes p of the form penta(n)-3, where penta(n) is the n-th pentagonal number.

2, 19, 67, 89, 173, 373, 587, 1423, 2377, 2749, 2879, 4027, 4507, 4673, 5189, 6899, 7523, 8623, 9319, 10289, 12373, 12647, 13487, 14947, 15859, 17117, 18757, 19777, 20123, 21179, 24509, 25673, 27673, 28909, 29327, 32779, 34123, 38317, 39769, 47969, 52919, 54623

Offset

1,1

Comments

The n-th pentagonal number is (3*n^2-n)/2 = n*(3*n-1)/2.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..8500

Example

a(2)= 19: n= 4: (3*n^2-n)/2-3= 19, which is prime.
a(6)= 373: n= 16: (3*n^2-n)/2-3= 373, which is prime.

Maple

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);

Mathematica

Select[Table[(n(3n-1))/2-3, {n, 2, 200}], PrimeQ] (* Harvey P. Dale, Jul 11 2015 *)

Crossrefs

Cf. A000326 (pentagonal numbers), A000040 (primes).

Sequence in context: A042149 A218547 A365494 * A309341 A079773 A217082

Adjacent sequences: A232534 A232535 A232536 * A232538 A232539 A232540

Keyword

nonn

Author

K. D. Bajpai, Nov 25 2013

Status

approved