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URL: https://oeis.org/A354156

⇱ A354156 - OEIS

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A354156
Primes p == 1 (mod 4) which are not Lagrange primes.
2
37, 61, 89, 101, 109, 113, 149, 157, 173, 181, 193, 197, 233, 269, 277, 293, 317, 337, 349, 353, 373, 389, 401, 421, 433, 509, 557, 569, 577, 593, 601, 613, 641, 673, 701, 709, 757, 761, 773, 797, 821, 829, 877, 881, 937, 941, 977, 1009, 1013, 1033, 1049, 1061
OFFSET
1,1
REFERENCES
J. B. Cosgrave, A Mersenne-Wieferich Odyssey, Manuscript, May 2022. See Section 18.5.
LINKS
PROG
(Python)
from itertools import islice
from sympy import factorial, nextprime
def agen(): # generator of terms
p = 5
while True:
X = (p-1)//2
Xf = factorial(X)**2
if any(pow(factorial(Y), 2, p)+1 == p for Y in range(X-1, 0, -1)):
yield p
p = nextprime(p)
while p%4 != 1:
p = nextprime(p)
print(list(islice(agen(), 5))) # Michael S. Branicky, May 30 2022
CROSSREFS
This is the complement of A354155 in A002144.
Sequence in context: A032627 A357955 A168006 * A385705 A139960 A103946
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 29 2022, based on Section 18.5 of Cosgrave (2022)
EXTENSIONS
a(26) and beyond from Michael S. Branicky, May 30 2022
STATUS
approved