A355809 - OEIS

%I #9 Jul 19 2022 10:43:15

%S 0,1,2,3,4,5,6,9,8,9,10,13,12,17,18,27,16,17,18,21,20,25,26,35,24,33,

%T 34,47,36,53,54,81,32,33,34,37,36,41,42,51,40,49,50,63,52,69,70,97,48,

%U 65,66,87,68,93,94,129,72,105,106,153,108,161,162,243,64,65

%N a(n) is the number at the apex of a triangle whose base contains the distinct powers of 2 summing to n (in ascending order), and each number in a higher row is the sum of the two numbers directly below it; a(0) = 0.

%H Rémy Sigrist, <a href="/A355809/b355809.txt">Table of n, a(n) for n = 0..8192</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) >= n with equality iff n = 0 or n belongs to A048645.

%F a(2*n) = 2*a(n).

%e For n = 27:

%e - we have the following triangle:

%e           47

%e         13  34

%e        3  10  24

%e      1   2   8  16

%e - so a(27) = 47.

%o (PARI) a(n) = { my (b=vector(hammingweight(n))); for (k=1, #b, n-=b[k]=2^valuation(n, 2)); while (#b>1, b=vector(#b-1, k, b[k+1]+b[k])); if (#b, b[1], 0) }

%Y See A355807 for similar sequences.

%Y Cf. A048645, A348296.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jul 18 2022