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A360805 Nonnegative integers k such that k! mod nextprime(k) is larger than k.

%I A360805 #41 Mar 10 2023 10:36:18
%S A360805 0,31,120,283,293,712,2872,3287,5028,5129,7088,9553,13229,14232,14799,
%T A360805 15113,20153,20830,23239,30233,31430,31667,34443,40654,44298,50184,
%U A360805 78877,105834,115281,125120,164253,192103,201590,227747,239910,241910,282230,322550,374370
%N A360805 Nonnegative integers k such that k! mod nextprime(k) is larger than k.
%H A360805 Chai Wah Wu, <a href="/A360805/b360805.txt">Table of n, a(n) for n = 1..213</a>
%F A360805 { k >= 0 : k! mod nextprime(k) > k }.
%F A360805 A360825(a(n)) > a(n).
%p A360805 q:= n-> is(n! mod nextprime(n)>n):
%p A360805 select(q, [$0..20000])[];
%o A360805 (Python)
%o A360805 from itertools import count, islice
%o A360805 from functools import reduce
%o A360805 from sympy import nextprime
%o A360805 def A360805_gen(startvalue=0): # generator of terms >= startvalue
%o A360805     n = max(startvalue,0)
%o A360805     m = nextprime(n)
%o A360805     while True:
%o A360805         a = m-1
%o A360805         klist = []
%o A360805         for i in range(m-1,n,-1):
%o A360805             a = a*pow(i,-1,m)%m
%o A360805             if a>i-1:
%o A360805                 klist.append(i-1)
%o A360805         yield from sorted(klist)
%o A360805         n, m = m, nextprime(m)
%o A360805 A360805_list = list(islice(A360805_gen(),30)) # _Chai Wah Wu_, Feb 24 2023
%Y A360805 Cf. A000142, A007978, A151800, A360825.
%K A360805 nonn
%O A360805 1,2
%A A360805 _Alois P. Heinz_, Feb 22 2023