A210482
Prime numbers of the form (p#)^2 + 1, where p# is a primorial.
Original entry on oeis.org
2, 5, 37, 44101, 5336101, 94083986096101, 1062053250251407755176413469419400772901
Offset: 1
2, 5 and 37 of A189409 are primes and in the sequence.
But 901=17*53, the next term of A189409, is not a prime and not in the sequence.
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from functools import reduce
import numpy as np
def factors(n):
return reduce(list._add_, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))
mul=1
for i in range(1,20):
if len(factors(i))<3:
mul*= i*i
if len(factors(mul+1))< 3:
print(mul+1)
A133834
Numbers k such that primorial(k)^4 + 1 is prime.
Original entry on oeis.org
0, 1, 2, 4, 23, 76, 339, 1282
Offset: 1
As primorial(2)^4 + 1 = (3*2)^4 + 1 = 1297 is prime, 2 is a term.
A264855
Integers n such that A002110(n)^2 - A002110(n) + 1 is prime.
Original entry on oeis.org
1, 2, 4, 5, 10, 14, 15, 20, 23, 46, 96, 281, 367, 542, 1380, 1395
Offset: 1
a(1) = 1 because 2^2 - 2 + 1 = 3 is prime.
a(2) = 2 because 6^2 - 6 + 1 = 31 is prime.
a(3) = 4 because 210^2 - 210 + 1 = 43891 is prime.
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Select[Range@ 400, PrimeQ[#^2 - # + 1 &@ Product[Prime@ k, {k, #}]] &] (* Michael De Vlieger, Nov 28 2015 *)
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a002110(n) = prod(k=1, n, prime(k));
for(n=0, 1e3, if(ispseudoprime(a002110(n)^2 - a002110(n) + 1), print1(n, ", ")))
Showing 1-3 of 3 results.
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