A302021 Numbers k such that k^2+1, (k+2)^2+1 and (k+6)^2+1 are prime.
4, 14, 124, 204, 464, 1144, 1314, 1564, 1964, 2454, 3134, 4174, 4364, 5584, 5874, 6234, 7804, 8174, 8784, 9874, 9894, 10424, 12354, 12484, 12874, 14034, 14194, 15674, 16224, 18274, 18994, 21134, 21344, 22344, 22624, 23134, 23784, 23944, 24974, 25554, 26504, 26934, 27064, 27804, 29364
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..200 from Seiichi Manyama)
Programs
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Magma
[n: n in [1..30000] | IsPrime(n^2+1) and IsPrime((n+2)^2+1) and IsPrime((n+6)^2+1)]; // Vincenzo Librandi, Apr 02 2018
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Maple
select(k->isprime(k^2+1) and isprime((k+2)^2+1) and isprime((k+6)^2+1),[$1..40000]); # Muniru A Asiru, Apr 02 2018
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Mathematica
Select[Range[1, 30000], PrimeQ[#^2 + 1] && PrimeQ[(# + 2)^2 + 1] && PrimeQ[(# + 6)^2 + 1] &] (* Vincenzo Librandi, Apr 02 2018 *)
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PARI
isok(k) = isprime(k^2+1) && isprime((k+2)^2+1) && isprime((k+6)^2+1); \\ Altug Alkan, Apr 02 2018
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Python
from sympy import isprime k, klist, A302021_list = 0, [isprime(i**2+1) for i in range(6)], [] while len(A302021_list) < 10000: i = isprime((k+6)**2+1) if klist[0] and klist[2] and i: A302021_list.append(k) k += 1 klist = klist[1:] + [i] # Chai Wah Wu, Apr 01 2018