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

1,1

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

Prog

(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)

Crossrefs

Sequence in context: A080508 A178141 A063987 * A010126 A021712 A307550

Adjacent sequences: A236266 A236267 A236268 * A236270 A236271 A236272

Keyword

nonn

Author

Ralf Stephan, Jan 21 2014

Status

approved