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.
a249858 n = a249857 n - a249856 n
import Data.List (delete)
a084937 n = a084937_list !! (n-1)
a084937_list = 1 : 2 : f 2 1 [3..] where
f x y zs = g zs where
g (u:us) | gcd y u > 1 || gcd x u > 1 = g us
| otherwise = u : f u x (delete u zs)
-- Reinhard Zumkeller, Jan 28 2012
N:= 1000: # to get a(n) until the first entry > N
a[1]:= 1: a[2]:= 2:
R:= {$3..N}:
for n from 3 while R <> {} do
success:= false;
for r in R do
if igcd(r,a[n-1]) = 1 and igcd(r,a[n-2])=1 then
a[n]:= r;
R:= R minus {r};
success:= true;
break
fi
od:
if not success then break fi;
od:
seq(a[i], i = 1 .. n-1); # Robert Israel, Dec 12 2014
lst={1,2,3}; unused=Range[4,100]; While[n=Select[unused, CoprimeQ[#, lst[[-1]]] && CoprimeQ[#, lst[[-2]]] &, 1]; n != {}, AppendTo[lst, n[[1]]]; unused=DeleteCases[unused, n[[1]]]]; lst
f[s_] := Block[{k = 1, l = Take[s, -2]}, While[ Union[ GCD[k, l]] != {1} || MemberQ[s, k], k++]; Append[s, k]]; Nest[f, {1, 2}, 67] (* Robert G. Wilson v, Jun 26 2011 *)
taken(k,t=v[k])=for(i=3,k-1, if(v[i]==t, return(1))); 0 step(k,g)=while(gcd(k,g)>1, k++); k first(n)=local(v=vector(n,i,i)); my(nxt=3,t); for(k=3,n, v[k]=step(nxt, t=v[k-1]*v[k-2]); while(taken(k), v[k]=step(v[k]+1,t)); if(v[k]==t, while(taken(k+1,t++),))); v \\ Charles R Greathouse IV, Aug 26 2016
from math import gcd A084937_list, l1, l2, s, b = [1,2], 2, 1, 3, set() for _ in range(10**3): i = s while True: if not i in b and gcd(i,l1) == 1 and gcd(i,l2) == 1: A084937_list.append(i) l2, l1 = l1, i b.add(i) while s in b: b.remove(s) s += 1 break i += 1 # Chai Wah Wu, Dec 09 2014
a249856 = sum . map (flip mod 2) . (uss !!)
uss = [] : [] : [] : f 2 1 [3..] where
f x y zs = g zs [] where
g (v:vs) ws | gcd v y > 1 || gcd v x > 1 = g vs (v : ws)
| otherwise = ws : f v x (delete v zs)
After step 7 of A084937, here is what we have: 1 2 3 4 5 6 7 ... n 1 2 3 5 4 7 9 ... A084937(n) so m = 9, and the missing numbers < 9 are 6 and 8, so a(7) = 2.
After step 7 of A084937, here is what we have: 1 2 3 4 5 6 7 ... n 1 2 3 5 4 7 9 ... A084937(n) so m = 9, and the missing even numbers < 9 are 6 and 8, so a(7) = 2.
After step 7 of A084937, here is what we have: 1 2 3 4 5 6 7 ... n 1 2 3 5 4 7 9 ... A084937(n) so m = 9, and the missing numbers < 9 are 6 and 8, both even, so a(7) = 0.
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