A124199 - OEIS

%I #17 Sep 19 2022 04:53:46

%S 13,19,43,53,89,103,151,229,251,349,433,463,593,701,739,859,1033,1223,

%T 1429,1483,1709,1889,1951,2143,2699,3001,3079,3319,3739,4003,4093,

%U 4463,4751,5563,5669,6553,7019,7873,8513,9043,10009,10151,10729,11173,11779

%N Primes of the form k(k+1)/2-2 (i.e., two less than triangular numbers).

%C Equal to primes of the form (k^2-17)/8. Also equal to primes p such that 8*p+17 is a square. - _Chai Wah Wu_, Jul 14 2014

%H Chai Wah Wu, <a href="/A124199/b124199.txt">Table of n, a(n) for n = 1..2000</a>.

%e The (first five triangular numbers)-2 are: -1,1,4,8,13. So a(1)=13 is the first prime of this form.

%t Pick[ #1, PrimeQ[ #1]]&[((1/2)*#1*(#1 + 1) - 2 & ) /@ Range[180]]

%t Select[Accumulate[Range[250]]-2,PrimeQ] (* _Harvey P. Dale_, Jun 07 2020 *)

%o (Python)

%o import sympy

%o [n*(n+1)/2-2 for n in range(10**6) if isprime(n*(n+1)/2-2)] # _Chai Wah Wu_, Jul 14 2014

%o (PARI) isok(p) = isprime(p) && ispolygonal(p+2, 3); \\ _Michel Marcus_, Sep 19 2022

%Y Cf. A055472.

%K easy,nonn

%O 1,1

%A Peter Pein (petsie(AT)dordos.net), Dec 07 2006