A236269 First differences of Stanley sequence S(0,4) (A005487).

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, 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, 5, 50, 5, 21, 18, 30, 1, 6, 5, 4, 6, 4, 1, 2, 20, 10, 4, 24, 3, 13, 5

Offset: 1

Author

Ralf Stephan, Jan 21 2014

Keywords

• nonn

Comments

Also first differences of Stanley sequence S(1,5) (A033158).

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.

Records are 4, 7, 17, 18, 26, 48, 50, 55, 76, 87, 92, 93, 165, 175,...

Positions of records are 1, 7, 16, 23, 28, 49, 61, 81, 83, 101, 147, 165, 185, 250, 400,...

Positions where a(n)=1: 2, 5, 12, 33, 35, 66, 72, 94, 125, 160, 189, 288, 307, 327,...

Links

• Ralf Stephan, Table of n, a(n) for n = 1..4650

Programs

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
S04(n)=N=1000;NAP([0,4],N)[n]
a(n)=S04(n+1)-S04(n)