A354156 Primes p == 1 (mod 4) which are not Lagrange primes.

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

Michael S. Branicky, Table of n, a(n) for n = 1..5383

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 * A139960 A103946 A107142

Adjacent sequences: A354153 A354154 A354155 * A354157 A354158 A354159

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