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
Keywords
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
Programs
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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
Extensions
a(26) and beyond from Michael S. Branicky, May 30 2022