A242702 -id:A242702 - cp's OEIS frontend

A242708 Primes p such that p^2 + p + 41 is semiprime.

41, 89, 109, 127, 163, 173, 239, 251, 271, 283, 331, 347, 349, 367, 373, 383, 389, 401, 409, 421, 443, 449, 463, 467, 487, 547, 557, 563, 569, 571, 577, 587, 593, 613, 643, 661, 701, 727, 733, 739, 761, 769, 773, 797, 823, 827, 853, 857, 881, 907, 937, 947, 971

Offset: 1

K. D. Bajpai, May 21 2014

nonn

n^2+n+41 is sometimes referred to as Euler's polynomial.
Subsequence of A228184.
A242702 is for semiprimes such that n^2+n+41 is also semiprime.

			41 is prime and 41^2 + 41 + 41 = 1763 = 41 * 43 is semiprime. Hence, 41 is in the sequence.
127 is prime and 127^2 + 127 + 41 = 16297 = 43 * 379 is semiprime. Hence, 127 is in the sequence.
43 is prime and 43^2 + 43 + 41 = 1933 which is prime (not semiprime). Hence, 43 is not in the sequence.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A001358, A228184, A238242, A242702.

with(numtheory): A242708:= proc();  if isprime(n) and bigomega(n^2+n+41)=2 then RETURN (n);  fi;  end: seq(A242708 (), n=1..1000);

c = 0; Do[If[PrimeQ[n] && PrimeOmega[n^2 + n + 41] == 2, c++; Print[c, "  ", n]], {n, 1, 3*10^5}];

cp's OEIS Frontend

A242708 Primes p such that p^2 + p + 41 is semiprime.

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