cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Ralf Stephan, Jan 30 2014

Keywords

Comments

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

Links

Crossrefs

Cf. A236269.

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

A185256 Stanley Sequence S(0,3).

Original entry on oeis.org

0, 3, 4, 7, 9, 12, 13, 16, 27, 30, 31, 34, 36, 39, 40, 43, 81, 84, 85, 88, 90, 93, 94, 97, 108, 111, 112, 115, 117, 120, 121, 124, 243, 246, 247, 250, 252, 255, 256, 259, 270, 273, 274, 277, 279, 282, 283, 286, 324, 327, 328, 331, 333, 336, 337, 340, 351, 354, 355, 358, 360, 363
Offset: 1

Views

Author

N. J. A. Sloane, Mar 19 2011

Keywords

Comments

Given a finite increasing sequence V = [v_1, ..., v_k] containing no 3-term arithmetic progression, the Stanley Sequence S(V) is obtained by repeatedly appending the smallest term that is greater than the previous term and such that the new sequence also contains no 3-term arithmetic progression.

Examples

			After [0, 3, 4, 7, 9] the next term cannot be 10 or we would have the 3-term A.P. 4,7,10; it cannot be 11 because of 7,9,11; but 12 is OK.

References

  • R. K. Guy, Unsolved Problems in Number Theory, E10.

Links

Crossrefs

For other examples of Stanley Sequences see A005487, A005836, A187843, A188052, A188053, A188054, A188055, A188056, A188057.
See also A004793, A033160, A033163.

Programs

  • Maple
    # Stanley Sequences, Discrete Math. vol. 311 (2011), see p. 560
ss:=proc(s1,M) local n,chvec,swi,p,s2,i,j,t1,mmm; t1:=nops(s1); mmm:=1000;
s2:=Array(1..t1+M,s1); chvec:=Array(0..mmm);
for i from 1 to t1 do chvec[s2[i]]:=1; od;
# Get n-th term:
for n from t1+1 to t1+M do # do 1
# Try i as next term:
for i from s2[n-1]+1 to mmm do # do 2
swi:=-1;
# Test against j-th term:
for j from 1 to n-2 do # do 3
p:=s2[n-j];
if 2*p-i < 0 then break; fi;
if chvec[2*p-i] = 1 then swi:=1; break; fi;
od; # od 3
if swi=-1 then s2[n]:=i; chvec[i]:=1; break; fi;
od; # od 2
if swi=1 then ERROR("Error, no solution at n = ",n); fi;
od; # od 1;
[seq(s2[i],i=1..t1+M)];
end;
ss([0,3],80);
  • Mathematica
    ss[s1_, M_] := Module[{n, chvec, swi, p, s2, i, j, t1, mmm}, t1 = Length[s1]; mmm = 1000; s2 = Table[s1, {t1 + M}] // Flatten; chvec = Array[0&, mmm];
For[i = 1, i <= t1, i++, chvec[[s2[[i]] ]] = 1];
(* get n-th term *)
For[n = t1+1, n <= t1 + M, n++,
(* try i as next term *)
For[i = s2[[n-1]] + 1, i <= mmm, i++, swi = -1;
(* test against j-th term *)
For[j = 1, j <= n-2, j++, p = s2[[n - j]]; If[2*p - i < 0, Break[] ];
If[chvec[[2*p - i]] == 1, swi = 1; Break[] ] ];
If[swi == -1, s2[[n]] = i; chvec[[i]] = 1; Break[] ] ];
If[swi == 1, Print["Error, no solution at n = ", n] ] ];
Table[s2[[i]], {i, 1, t1 + M}] ];
ss[{0, 3}, 80] (* Jean-François Alcover, Sep 10 2013, translated from Maple *)
  • PARI
    A185256(n,show=1,L=3,v=[0,3], D=v->v[2..-1]-v[1..-2])={while(#v1||next(2), 2); break)); if(type(show)=="t_VEC", v, v[n])} \\ 2nd (optional) arg: zero = silent, nonzero = verbose, vector (e.g. [] or [1]) = get the whole list [a(1..n)] as return value, else just a(n). - M. F. Hasler, Jan 18 2016

A267650 Stanley sequence S_4(0,3): lexicographic first increasing sequence with a(0) = 0, a(1) = 3 and no 4 terms in arithmetic progression.

Original entry on oeis.org

0, 3, 4, 5, 7, 8, 10, 11, 16, 17, 18, 20, 21, 27, 28, 29, 31, 32, 34, 35, 36, 53, 55, 56, 57, 60, 61, 62, 64, 67, 69, 75, 87, 91, 100, 101, 103, 104, 105, 108, 109, 110, 114, 116, 120, 125, 127, 128, 129, 132, 134, 135, 164, 168, 173, 174, 175, 177, 181, 182, 184, 188, 190
Offset: 0

Views

Author

M. F. Hasler, Jan 18 2016

Keywords

Comments

See A185256 for S(0,3) = S_3(0,3) and A266728 for S_5(0,3).

Links

Crossrefs

For other examples of Stanley Sequences see A005487, A005836, A187843, A188052, A188053, A188054, A188055, A188056, A188057, A266727, A266728.
See also A004793, A033160, A033163.

Programs

  • PARI
    a(n,show=1,L=4,v=[0,3], D=v->v[2..-1]-v[1..-2])={while(#v<=n, show&&print1(v[#v]", "); v=concat(v, v[#v]); while(v[#v]++, forvec(i=vector(L, j, [if(j1||next(2), 2); break)); if(type(show)=="t_VEC", v, v[n+1])} \\ 2nd (optional) arg: zero = silent, nonzero = verbose, vector (e.g. [] or [1]) = get the whole list [a(1..n)] as return value, else just a(n). - M. F. Hasler, Jan 18 2016
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.