A262182 Prime numbers of the form (n*(n+1)/2)^2 + 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
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..5231
Programs
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Mathematica
Select[Accumulate[Range[250]]^2+1,PrimeQ] (* Harvey P. Dale, Nov 14 2024 *)
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PARI
for(n=1, 1e3, if(isprime(k = (n*(n+1)/2)^2+1), print1(k", "))) \\ Altug Alkan, Oct 02 2015
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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
Formula
Extensions
More terms from Altug Alkan, Oct 02 2015
Comments