A236269 -id:A236269 - cp's OEIS frontend

A236774 A236269(n) - A236313(n).

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, 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, -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

Offset: 1

Ralf Stephan, Jan 31 2014

sign

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.

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...

Ralf Stephan, Table of n, a(n) for n = 1..4599

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
v=NAP([0,4],5000)
a(n)=v[n+1]-v[n]-(3^valuation(n,2)+1)/2

A231990 First differences of Stanley sequence S(0,5) (A187843).

Original entry on oeis.org

5, 1, 2, 1, 5, 1, 2, 10, 4, 1, 4, 2, 4, 1, 8, 14, 8, 1, 8, 7, 11, 1, 6, 2, 14, 29, 2, 11, 9, 3, 2, 11, 8, 13, 5, 4, 7, 6, 3, 24, 59, 9, 7, 1, 20, 5, 1, 8, 3, 33, 27, 11, 9, 12, 3, 2, 11, 9, 27, 4, 2, 5, 12, 1, 5, 16, 54, 80, 37, 15, 1, 6, 3, 33, 3, 17, 5, 9, 17, 1, 35, 32, 2, 72, 10, 3, 82, 6, 4, 6, 5, 2, 1, 5, 31, 14, 13

Offset: 1

Ralf Stephan, Jan 30 2014

nonn

For known formulas of differences of other Stanley sequences see A093682.

Ralf Stephan, Table of n, a(n) for n = 1..999

Cf. A236269.

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
S05(n)=N=1000;NAP([0,5],N)[n]
a(n)=S05(n+1)-S05(n)

cp's OEIS Frontend

A236774 A236269(n) - A236313(n).

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