A356110
Numbers k such that k^2 + {1,3,7,13,31} are prime.
Original entry on oeis.org
4, 10, 14290, 43054, 109456, 315410, 352600, 483494, 566296, 685114, 927070, 1106116, 1248796, 1501174, 1997986, 2399204, 2501404, 2553100, 2726840, 2874680, 3291760, 4129394, 4473766, 4794520, 4901144, 6350306, 7444070, 7753456, 7892504, 8009536, 8069540
Offset: 1
4^2 + {1,3,7,13,31} = {17,19,23,29,47} are all prime.
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q:= k-> andmap(j-> isprime(k^2+j), [1,3,7,13,31]):
select(q, [$0..1000000])[]; # Alois P. Heinz, Jul 27 2022
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Select[Range[10^6], AllTrue[#^2 + {1,3,7,13,31}, PrimeQ] &] (* Amiram Eldar, Jul 27 2022 *)
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from sympy import isprime
def ok(n): return all(isprime(n*n+i) for i in {1,3,7,13,31})
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 27 2022
A356175
Numbers k such that k^2 + {1,3,7,13,163} are prime.
Original entry on oeis.org
2, 4, 10, 14290, 64390, 74554, 83464, 93460, 132304, 238850, 262630, 277630, 300206, 352600, 376190, 404954, 415180, 610340, 806180, 984686, 1025650, 1047050, 1106116, 1382860, 2014624, 2440714, 2525870, 2538344, 2760026, 2826380, 3145600, 3508586, 3715156
Offset: 1
2 is a term since 2^2 + {1,3,7,13,163} = {5,7,11,17,167} are all primes.
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q:= k-> andmap(j-> isprime(k^2+j), [1, 3, 7, 13, 163]):
select(q, [$0..1000000])[]; # Alois P. Heinz, Jul 28 2022
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Select[Range[4*10^6], AllTrue[#^2 + {1, 3, 7, 13, 163}, PrimeQ] &] (* Amiram Eldar, Jul 28 2022 *)
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is(k)=my(v=[1,3,7,13,163],ok=1);for(i=1,#v,if(!isprime(k^2+v[i]),ok=0;break));ok
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from sympy import isprime
def ok(n): return all(isprime(n*n+i) for i in {1,3,7,13,163})
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 28 2022
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