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A371980
Sophie Germain primes p such that 4*p + 3 is a composite number.
0
3, 23, 29, 53, 83, 113, 131, 173, 191, 233, 239, 251, 281, 293, 419, 431, 443, 491, 593, 641, 653, 659, 683, 743, 761, 809, 911, 953, 1013, 1049, 1103, 1223, 1289, 1439, 1499, 1559, 1583, 1601, 1733, 1973, 2003, 2039, 2063, 2069, 2129, 2141, 2273, 2339, 2351, 2393, 2399, 2543, 2549, 2693, 2741, 2753
OFFSET
1,1
EXAMPLE
a(1) = 3 is prime and 2*3 + 1 = 7 also but not 4*3 + 3 = 15.
MATHEMATICA
Select[Prime[Range[410]], And[PrimeQ[2 # + 1], CompositeQ[4 # + 3]] &] (* Michael De Vlieger, Apr 19 2024 *)
PROG
(Python)
import sympy as sp
l = []
for i in range(2, 2800):
if sp.isprime(i) and sp.isprime(2*i + 1) and not(sp.isprime(4*i + 3)):
l.append(i)
print(l)
CROSSREFS
Cf. A005384.
Sequence in context: A136090 A032688 A142345 * A217329 A133023 A098946
KEYWORD
nonn
AUTHOR
Alexandre Herrera, Apr 15 2024
STATUS
approved