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A252669 a(n) is the smallest integer k such that n*k mod (n+k) = 1, or -1 if no such k exists.

%I A252669 #32 Nov 13 2024 13:52:27
%S A252669 1,3,2,13,8,31,3,5,32,91,50,17,4,183,98,241,12,7,162,381,5,75,30,553,
%T A252669 288,651,46,129,392,23,6,9,76,55,578,1261,100,47,722,1561,17,311,7,
%U A252669 105,968,27,18,413,1152,11,1250,489,228,2863,34,3081,8,615,1682,217,1800,707
%N A252669 a(n) is the smallest integer k such that n*k mod (n+k) = 1, or -1 if no such k exists.
%F A252669 a(a(n)) <= n.
%t A252669 sik[n_]:=Module[{k=1},While[Mod[n*k,n+k]!=1,k++];k]; Array[sik,70] (* _Harvey P. Dale_, Aug 15 2015 *)
%o A252669 (Python)
%o A252669 import math
%o A252669 for n in range(1,333):
%o A252669     res=-1
%o A252669     for k in range(2**31-1):
%o A252669         if ((n*k) % (n+k) == 1):
%o A252669             res=k
%o A252669             break
%o A252669     print(res, end=', ')
%o A252669 (PARI) a(n) = k=1; while ((n*k) % (n+k) != 1, k++); k; \\ _Michel Marcus_, Jan 08 2015
%Y A252669 Cf. A063427.
%K A252669 nonn
%O A252669 1,2
%A A252669 _Alex Ratushnyak_, Jan 02 2015