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A236774 A236269(n) - A236313(n). 1

%I

%S 3,-1,1,-1,0,2,6,-11,4,0,3,-4,5,3,6,-24,4,0,4,5,3,5,17,-10,2,3,6,21,

%T 18,7,5,-105,0,3,0,6,8,10,9,-7,7,1,14,1,1,1,5,-23,47,5,4,20,11,19,10,

%U -10,20,0,5,0,49,3,20,-347,29,-1,5,0,3,4,3,-13,1,18,9,-1,23,1,12,-36,54,0,75,16,2,5,40

%N A236269(n) - A236313(n).

%C Known formulas for first differences of Stanley sequences are sums with one term always being A236313(n), so it makes sense in order to find a formula for the first differences of the Stanley sequence S[0,4] to subtract A236313(n) from that and look if something shows.

%C a(n) is negative for n = 2,4,8,12,16,24,32,40,48,56,64,66,72... and it appears that n is always even if a(n) is negative. It also seems that a(n) is always negative if n is a power of two, with a(2^m) = -1,-1,-11,-24,-105,-347,-1073,-3260,-9839,-29467,-85479,-265530...

%H Ralf Stephan, <a href="/A236774/b236774.txt">Table of n, a(n) for n = 1..4599</a>

%o (PARI)

%o NAP(sv,N)=local(v,vv,m,k,l,sl,vvl);sl=length(sv);vvl=min(N*N,10^6);v=vector(N);vv=vector(vvl);for(k=1,sl,v[k]=sv[k];for(l=1,k-1,vv[2*v[k]-v[l]]=1));m=v[sl]+1;for(k=sl+1,N,while(m<=vvl&&vv[m],m=m+1);if(m>vvl,return(v));for(l=1,k-1,sl=2*m-v[l];if(sl<=vvl,vv[sl]=1));vv[m]=1;v[k]=m);v

%o v=NAP([0,4],5000)

%o a(n)=v[n+1]-v[n]-(3^valuation(n,2)+1)/2

%K sign

%O 1,1

%A _Ralf Stephan_, Jan 31 2014

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Last modified January 28 06:26 EST 2022. Contains 350654 sequences. (Running on oeis4.)