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.
After 1 3 9 26 62 ------ 2 6 17 36 ------- 4 11 19 -------- 7 8 the next free number is 10 which we CAN add to 4th row.
Fold[Append[#1, #1[[#2]] + Complement[Range[Max@#1 + 1], #1][[#2]]] &, {2}, Range[50]] (* Ivan Neretin, Apr 04 2016 *)
s:= proc() false end: b:= proc() false end:
a:= proc(n) option remember; local i, k;
if n=1 then b(1):= true; 1
else for k while b(k) or s(k) or
(t-> b(t) or t=k)(abs(a(n-1)-k)) do od;
for i to n-1 do s(a(i)+k):= true od;
b(k), b(abs(a(n-1)-k)):= true$2; k
fi
end:
seq(a(n), n=1..101);
s[] = False; b[] = False; a[n_] := a[n] = Module[{i, k}, If[n == 1, b[1] = True; 1, For[k = 1, b[k] || s[k] || Function[t, b[t] || t == k][Abs[a[n-1]-k]], k++]; For[i = 1, i <= n-1, i++, s[a[i]+k] = True]; {b[k], b[Abs[a[n-1]-k]]} = {True, True}; k]]; Array[a, 101] (* Jean-François Alcover, Oct 28 2020, after Maple *)
s:= proc() false end: b:= proc() false end:
a:= proc(n) option remember; local i, k, ok;
if n=1 then b(1):= true; 1
else for k do if b(k) or s(k) or (t-> b(t) or t=k)(
abs(a(n-1)-k)) then next fi; ok:=true;
for i to n-1 while ok do if b(k+a(i))
then ok:=false fi od; if ok then break fi
od;
for i to n-1 do s(a(i)+k):= true od;
b(k), b(abs(a(n-1)-k)):= true$2; k
fi
end:
seq(a(n), n=1..101);
s[] = False; b[] = False; a[n_] := a[n] = Module[{i, k, ok}, If[n == 1, b[1] = True; 1, For[k = 1, True, k++, If[b[k] || s[k] || Function[t, b[t] || t == k][Abs[a[n-1] - k]], Continue[]]; ok = True; For[i = 1, i <= n-1 && ok, i++, If[b[k + a[i]], ok = False]]; If[ok, Break[]]]; For[i = 1, i <= n-1, i++, s[a[i] + k] = True]; {b[k], b[Abs[a[n-1] - k]]} = {True, True}; k]]; Table[a[n], {n, 1, 101}] (* Jean-François Alcover, Jul 16 2021, after Alois P. Heinz *)
import Data.List (transpose) a156031 n = a156031_list !! n a156031_list = tail $ concat (transpose [a022941_list, a143344_list]) -- Reinhard Zumkeller, May 17 2013
f="b156031.txt"; used=[]; write(f,c=1," ",b=1);a=1; for(i=1,1e3, used=setunion(used,Set(a+=b)); while(setsearch(used,b++), used=setminus(used,Set(b))); write(f,c++," "a"\n",c++," "b)) \\ M. F. Hasler, Nov 01 2009
# Based on Christopher Carl Heckman's program for A225376. f:=proc(N) local h,dh,ddh,S,mex,i; h:=1,3,9; dh:=2,6; ddh:=4; mex:=5; S:={h,dh,ddh}; for i from 4 to N do while mex in S do S:=S minus {mex}; mex:=mex+1; od; ddh:=ddh,mex; dh:=dh,dh[-1]+mex; h:=h,h[-1]+dh[-1]; S:=S union {h[-1], dh[-1], ddh[-1]}; mex:=mex+1; od; RETURN([[h],[dh],[ddh]]); end; f(100);
f[N_] := Module[{P = {1, 3, 9}, Q = {2, 6}, R = {4}, S, mex = 5, i},
S = Join[P, Q, R];
For[i = 4, i <= N, i++,
While[MemberQ[S, mex], S = S~Complement~{mex}; mex++];
AppendTo[R, mex];
AppendTo[Q, Q[[-1]] + mex];
AppendTo[P, P[[-1]] + Q[[-1]]];
S = S~Union~{P[[-1]], Q[[-1]], R[[-1]]}; mex++];
P];
f[100] (* Jean-François Alcover, Mar 06 2023, after Maple code *)
See A225385.
See A225385.
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