cp's OEIS Frontend

A355807 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 absolute difference of the two numbers directly below it; a(0) = 0.

%I A355807 #12 Jul 19 2022 10:43:34
%S A355807 0,1,2,1,4,3,2,1,8,7,6,5,4,1,2,1,16,15,14,13,12,9,10,9,8,1,2,3,4,3,2,
%T A355807 1,32,31,30,29,28,25,26,25,24,17,18,13,20,19,18,17,16,1,2,11,4,5,6,3,
%U A355807 8,7,6,3,4,1,2,1,64,63,62,61,60,57,58,57,56,49,50
%N A355807 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 absolute difference of the two numbers directly below it; a(0) = 0.
%C A355807 This sequence has similarities with A334387.
%H A355807 Rémy Sigrist, <a href="/A355807/b355807.txt">Table of n, a(n) for n = 0..8191</a>
%H A355807 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A355807 a(n) <= n with equality iff n = 0 or n is a power of 2.
%F A355807 a(2*n) = 2*a(n).
%e A355807 For n = 27:
%e A355807 - we have the following triangle:
%e A355807             3
%e A355807           5   2
%e A355807         1   6   8
%e A355807       1   2   8  16
%e A355807 - so a(27) = 3.
%o A355807 (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, abs(b[k+1]-b[k]))); if (#b, b[1], 0) }
%Y A355807 See A355808, A355809, A355810 and A355811 for other variants.
%Y A355807 Cf. A133457, A334387, A348296.
%K A355807 nonn,base
%O A355807 0,3
%A A355807 _Rémy Sigrist_, Jul 18 2022