cp's OEIS Frontend

A262182 Prime numbers of the form (n*(n+1)/2)^2 + 1.

%I A262182 #64 Nov 14 2024 14:43:39
%S A262182 2,37,101,1297,4357,14401,44101,90001,164837,246017,608401,894917,
%T A262182 1382977,4326401,8122501,8561477,9985601,10497601,38638657,46049797,
%U A262182 52707601,84272401,121572677,146168101,165894401,201526417,259532101,289680401,404010001,428738437
%N A262182 Prime numbers of the form (n*(n+1)/2)^2 + 1.
%C A262182 Sum_{n>=1} 1/a(n) = 0.538046187...
%H A262182 Chai Wah Wu, <a href="/A262182/b262182.txt">Table of n, a(n) for n = 1..5231</a>
%F A262182 a(n) = A154323(A217755(n)). - _Michel Marcus_, Oct 02 2015
%F A262182 a(n) = ((A217755(n)^2 + A217755(n))/2)^2 + 1. - _Jean C. Lambry_, Oct 07 2015
%t A262182 Select[Accumulate[Range[250]]^2+1,PrimeQ] (* _Harvey P. Dale_, Nov 14 2024 *)
%o A262182 (Python)
%o A262182 def prime(n):
%o A262182     if n == 1: return True
%o A262182     d = n + 1
%o A262182     c = n - 1
%o A262182     while c > 0 and d % c:
%o A262182         d += n
%o A262182         c -= 1
%o A262182     return bool(c == 1)
%o A262182 n = 1
%o A262182 i = 1
%o A262182 while i <= 500:
%o A262182     target = (i * (i + 1)) // 2
%o A262182     if prime(target):
%o A262182         print(n, target*target+1)
%o A262182         n += 1
%o A262182     i += 1
%o A262182 # _Jean C. Lambry_, Oct 06 2015
%o A262182 (PARI) for(n=1, 1e3, if(isprime(k = (n*(n+1)/2)^2+1), print1(k", "))) \\ _Altug Alkan_, Oct 02 2015
%Y A262182 Cf. A154323, A217755.
%K A262182 nonn
%O A262182 1,1
%A A262182 _Jean C. Lambry_, Oct 02 2015
%E A262182 More terms from _Altug Alkan_, Oct 02 2015