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%I #17 Feb 07 2014 05:35:52
%S 4,1,2,4,1,4,7,3,5,2,4,1,6,5,7,17,5,2,5,10,4,7,18,4,3,5,7,26,19,9,6,
%T 17,1,5,1,11,9,12,10,7,8,3,15,6,2,3,6,18,48,7,5,25,12,21,11,4,21,2,6,
%U 5,50,5,21,18,30,1,6,5,4,6,4,1,2,20,10,4,24,3,13,5
%N First differences of Stanley sequence S(0,4) (A005487).
%C Also first differences of Stanley sequence S(1,5) (A033158).
%C While there are conjectures about formulas for S(0,m), m=1,2,3,6,9... (see A093682), m=4 is the first case where the first differences look almost random.
%C Records are 4, 7, 17, 18, 26, 48, 50, 55, 76, 87, 92, 93, 165, 175,...
%C Positions of records are 1, 7, 16, 23, 28, 49, 61, 81, 83, 101, 147, 165, 185, 250, 400,...
%C Positions where a(n)=1: 2, 5, 12, 33, 35, 66, 72, 94, 125, 160, 189, 288, 307, 327,...
%H Ralf Stephan, <a href="/A236269/b236269.txt">Table of n, a(n) for n = 1..4650</a>
%o (PARI) NAP(sv,N)=local(v,vv,m,k,l,sl,vvl);sl=length(sv);vvl=min(N*N,10^5);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 S04(n)=N=1000;NAP([0,4],N)[n]
%o a(n)=S04(n+1)-S04(n)
%K nonn
%O 1,1
%A _Ralf Stephan_, Jan 21 2014
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