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 A290171 Numbers k such that (k-1)^2 < (k-1)! mod k^2. 0
 5, 13, 563, 1277, 780887 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Wilson primes (A007540) are terms of this sequence. a(n) is prime or twice a prime. Otherwise (k-1)! mod k^2 = 0 for k > 9 where k is not a prime and not twice a prime. - David A. Corneth, Jul 23 2017 LINKS MATHEMATICA Select[Range[10^4], (#-1)^2 2, return(0), if(#f~==2, if(f[1, 1]!=2, return(0)))); forprime(p=2, n-1, r*=Mod(p, n^2)^val(n-1, p)); (n-1)^2 < lift(r) \\ David A. Corneth, Jul 23 2017 (Python) def ok(n):     nn = n**2; f = 1%nn     for k in range(1, n): f = f*k%nn     return (n-1)**2 < f print(list(filter(ok, range(1, 1300)))) # Michael S. Branicky, Jul 23 2021 (Python) # faster for initial segment of sequence from math import factorial def afind(limit, startk=1):     k = startk; kkprev = (k-1)**2; f = factorial(k-1)     while k < limit:         kk = k*k         if kkprev < f%kk: print(k, end=", ")         kkprev = kk; f *= k; k += 1 afind(10000) # Michael S. Branicky, Jul 25 2021 CROSSREFS Cf. A007540. Sequence in context: A145557 A012033 A007540 * A157250 A009157 A153374 Adjacent sequences:  A290168 A290169 A290170 * A290172 A290173 A290174 KEYWORD nonn,hard,more AUTHOR Gionata Neri, Jul 23 2017 EXTENSIONS a(5) from Chai Wah Wu, Jul 30 2017 STATUS approved

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Last modified August 12 13:59 EDT 2022. Contains 356077 sequences. (Running on oeis4.)