A256135 - OEIS

%I #31 Feb 28 2017 22:47:14

%S 1,5,5,25,5,25,25,125,5,25,25,125,25,125,125,625,5,25,25,125,25,125,

%T 125,625,25,125,125,625,125,625,625,3125,5,25,25,125,25,125,125,625,

%U 25,125,125,625,125,625,625,3125,25,125,125,625,125,625,625,3125,125,625,625,3125,625,3125,3125,15625

%N a(n) = 5^A000120(n).

%C Also, a row of the square array A256140.

%C It appears that when A151780 is regarded as a triangle in which the row lengths are the powers of 2, this is what the rows converge to.

%F a(n) = A000351(A000120(n)). - _Michel Marcus_, Mar 21 2015

%F G.f.: Product_{k>=0} (1 + 5*x^(2^k)). - _Ilya Gutkovskiy_, Feb 28 2017

%e Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:

%e 1;

%e 5;

%e 5, 25;

%e 5, 25, 25, 125;

%e 5, 25, 25, 125, 25, 125, 125, 625;

%e ...

%t 5^# & /@ Nest[Join[#, # + 1] &, {0}, 6] (* _Michael De Vlieger_, Mar 20 2015, after _IWABUCHI Yu(u)ki_ at a000120 *)

%o (PARI) a(n) = 5^hammingweight(n); \\ _Michel Marcus_, Mar 21 2015

%Y Cf. A000120, A001316, A048883, A102376, A130667, A151780, A256140, A256141.

%K nonn

%O 0,2

%A _Omar E. Pol_, Mar 19 2015

%E More terms from _Michael De Vlieger_, Mar 20 2015