A067999
Numbers k such that (k! - 1) == 0 (mod prime(k)).
Original entry on oeis.org
1, 3, 10, 149, 437
Offset: 1
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f[n_] := Block[{k = p = 1, m = Prime[n]}, While[p = Mod[p k, m]; k < n, k++ ]; p]; Do[ If[ f[n] == 1, Print[n]], {n, 100000}] (* Robert G. Wilson v, Mar 16 2004 *)
A066953
Integers of the form (k!+1)/prime(k).
Original entry on oeis.org
1, 1, 11, 104956945995541, 6458007542034006723505363870885661685813595082173513446600259282126155549185667752443
Offset: 1
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f[k_] := (k! + 1)/Prime[k]; f /@ Select[Range[100], IntegerQ[f[#]] &] (* Amiram Eldar, Apr 22 2025 *)
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list(lim) = {my(k = 0, r = 1); forprime(p = 1, lim, k++; r *= k; if(!((r+1) % p), print1((r+1)/p, ", ")));} \\ Amiram Eldar, Apr 22 2025
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