b.sf

#!/usr/bin/ruby

# https://oeis.org/A309285

# a(6) <= 35141256146761030267, a(7) <= 4951782572086917319747. - ~~~~

# A309285(6) <= 35141256146761030267
# A309285(7) <= 4951782572086917319747

func isok_a(n, k) {
    # prime(n)^((k-1)/2) == -1 (mod k)
    powmod(prime(n), ((k-1)/2), k) == 1 && (
        primes(prime(n)-1) -> all {|b|
                powmod(b, (k-1)/2, k).is_congruent(-1, k)
        }
    )
}

#~ var n = 1
#~ for k in (1..1e6) {
    #~ k.is_composite || next
    #~ if (isok_a(n, k)) {
        #~ say "a(#{n}) = #{k}"
        #~ ++n
    #~ }
#~ }

say isok_a(7, 4951782572086917319747)

# isok(n,k) = (k%2==1) && !isprime(k) && Mod(prime(n), k)^((k-1)/2) == Mod(1, k) && !forprime(q=2, prime(n)-1, if(Mod(q, k)^((k-1)/2) != Mod(-1, k), return(0)));
# a(n) = for(k=9, oo, if(isok(n, k), return(k))); \\ ~~~~

# b^((a(n)-1)/2) == (b/a(n)) (mod a(n)) for every natural b <= prime(n), where (x/y) is the Jacobi symbol.