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%I #40 Oct 09 2019 04:30:05
%S 1,2,9,8744,8189,19531249994,731,52,1745,26,63,1290,10735,38,237,214,
%T 5417,3722,49,452,109,2818,45,990,227,368,47,78704,533,342,8437,44,
%U 11467,134,95,368,5077,1886,83,68626,89,1964,426398815,1156636,5719,25334,4835,542
%N a(n) is the smallest m > n such that m + n divides m^(m - n)*(m - n)^m + 1.
%e a(0) = 1 because 1 + 0 = 1 divides 0^(1 - 0)*(1 - 0)^0 + 1 = 1;
%e a(1) = 2 because 2 + 1 = 3 divides 2^(2 - 1)*(2 - 1)^2 + 1 = 3;
%e a(2) = 9 because 9 + 2 = 11 divides 9^(9 - 2)*(9 - 2)^9 + 1 = 4782969*40353607 + 1 = 193010051319184.
%t a[5] = 19531249994; a[n_] := Block[{k = n + 1}, While[ Mod[ PowerMod[k, k-n, k+n] PowerMod[k-n, k, k+n] + 1, k+n] != 0, k++]; k]; a /@ Range[0, 40] (* _Giovanni Resta_, Oct 08 2019 *)
%o (PARI) a(n) = my(m=n+1); while ((m^(m - n)*(m - n)^m + 1) % (m+n), m++); m; \\ _Michel Marcus_, Oct 08 2019
%K nonn
%O 0,2
%A _Juri-Stepan Gerasimov_, Oct 07 2019
%E a(5) and a(39)-a(47) from _Giovanni Resta_, Oct 08 2019
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