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A262182
Prime numbers of the form (n*(n+1)/2)^2 + 1.
1
2, 37, 101, 1297, 4357, 14401, 44101, 90001, 164837, 246017, 608401, 894917, 1382977, 4326401, 8122501, 8561477, 9985601, 10497601, 38638657, 46049797, 52707601, 84272401, 121572677, 146168101, 165894401, 201526417, 259532101, 289680401, 404010001, 428738437
OFFSET
1,1
COMMENTS
Sum_{n>=1} 1/a(n) = 0.538046187...
FORMULA
a(n) = A154323(A217755(n)). - Michel Marcus, Oct 02 2015
a(n) = ((A217755(n)^2 + A217755(n))/2)^2 + 1. - Jean C. Lambry, Oct 07 2015
PROG
(Python)
def prime(n):
if n == 1: return True
d = n + 1
c = n - 1
while c > 0 and d % c:
d += n
c -= 1
return bool(c == 1)
n = 1
i = 1
while i <= 500:
target = (i * (i + 1)) // 2
if prime(target):
print(n, target*target+1)
n += 1
i += 1
# Jean C. Lambry, Oct 06 2015
(PARI) for(n=1, 1e3, if(isprime(k = (n*(n+1)/2)^2+1), print1(k", "))) \\ Altug Alkan, Oct 02 2015
CROSSREFS
Sequence in context: A309429 A374919 A258896 * A142077 A107182 A134596
KEYWORD
nonn
AUTHOR
Jean C. Lambry, Oct 02 2015
EXTENSIONS
More terms from Altug Alkan, Oct 02 2015
STATUS
approved