A229960 Primes of the form n^3 - T(n) - 1 where T(n) is the n-th triangular number.

53, 109, 683, 4759, 7789, 9029, 13523, 15299, 45989, 63179, 68059, 90089, 116423, 174019, 225089, 370619, 610469, 700963, 994949, 1025149, 1119403, 1398599, 1594709, 1898873, 2291189, 2561899, 2734129, 2975543, 3038039, 3296773, 3784169, 3857489, 5913269, 6212483

Offset: 1

Author

K. D. Bajpai, Oct 04 2013

Keywords

• nonn
• less

Comments

Also primes of the form (2*n^3 - n^2 - n - 2)/2.

Examples

			a(2) = 109 since 5^3 - T(5) - 1 = 125 - 15 - 1 = 109, which is prime.
a(6) = 9029 since 21^3 - T(21) - 1 = 9261 - 231 - 1 = 9029 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A229157, A229080.

Programs

Maple

KD:= proc() local a,b,d; a:= n^3;b:=(1/2)*n*(n+1); d:=a-b-1; if isprime(d) then   RETURN(d): fi;end: seq(KD(),n=1..500);

Mathematica

Select[Table[(n^3) - (n/2*(n + 1)) - 1, {n, 200}], PrimeQ]