A338151 a(n) = (n+1)^A338136(n) mod n^A338150(n).

9, 4, 9, 16, 25, 169, 25, 64, 81, 100, 25, 27, 729, 121, 49, 256, 289, 324, 81, 64, 243, 484, 49, 576, 5929, 676, 169, 784, 121, 125, 225, 100, 1089, 841, 7921, 1000, 343, 196, 81, 1600, 169, 216, 441, 361, 2025, 2116, 289, 2304, 2401, 256, 625, 2704, 2809, 441

Offset

2,1

Comments

a(n) is a perfect power, and a(n) == 1 + n*A338136(n) (mod n^2).

Links

Jinyuan Wang, Table of n, a(n) for n = 2..1000

Formula

a(n) = (n+1)^A338136(n) mod n^A338150(n).

Example

a(2) = 3^A338136(2) mod 2^A338150(2) = 3^6 mod 2^4 = 3^2 = 9.
a(13) = 14^A338136(13) mod 13^A338150(13) = 14^2 mod 13^2 = 3^3 = 27.

Maple

g:= proc(n) local k, x, j, F;
  for k from 2 to n-2 do
   x:= (n+1)^k;
   for j from 2 to floor(k*log[n](n+1)) do
     F:= ifactors(x mod (n^j))[2];
     if igcd(op(map(t -> t[2], F))) > 1 then return x mod (n^j) fi
  od od
end proc:
g(2):= 9: g(3):= 4:
map(g, [$2..40]);

Crossrefs

Cf. A338136, A338150.

Sequence in context: A355563 A332500 A253203 * A255642 A088701 A153698

Adjacent sequences: A338148 A338149 A338150 * A338152 A338153 A338154

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 12 2020

Status

approved