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.
list_A160218(n)={ my(a1=1,a2=1,S=[]); until( isprime(a1) & !print1(#S,",") & !n--, for( a=1,9e9, a*a1%a2 & next; setsearch(S,a) & next; a2=a1; S=setunion(S,Set(a1=a)); /*print1(a",");*/ next(2)); error);vecsort(eval(S)) }
from sympy import gcd def A151413(n): if n <= 2: return n else: l1, l2, m, b = 2, 1, 1, {1, 2} for j in range(3, 10**9): i = m while True: if not i in b: if i == n: return j l1, l2, m = i, l1, l1//gcd(l1, i) b.add(i) break i += m return "search limit reached." # Chai Wah Wu, Dec 09 2014
bb:= proc(n) option remember; false end: b:= proc(n) option remember; local k, m; if n<3 then bb(n):= true; n else m:= denom(b(n-1) /b(n-2)); for k from m by m while bb(k) do od; bb(k):= true; k fi end: a:= n-> numer(b(n-2) /b(n-1)): seq(a(n), n=3..100); # Alois P. Heinz, May 17 2009
bb[n_] := bb[n] = False;
b[n_] := b[n] = Module[{k, m}, If[n < 3, bb[n] = True; n, m = Denominator[ b[n - 1] /b[n - 2]]; For[ k = m , bb[k], k += m]; bb[k] = True; k ]];
a[n_] := Numerator[b[n - 2] /b[n - 1]];
Table[a[n], {n, 3, 100}]
bb:= proc(n) option remember; false end: b:= proc(n) option remember; local k, m; if n<3 then bb(n):= true; n else m:= denom(b(n-1) /b(n-2)); for k from m by m while bb(k) do od; bb(k):= true; k fi end: a:= n-> b(n+2) *b(n+1) /b(n): seq(a(n), n=1..100); # Alois P. Heinz, May 18 2009
bb[_] = False;
b[n_] := b[n] = Module[{k, m}, If[n<3, bb[n] = True; n, m = Denominator[ b[n-1]/b[n-2]]; For[k = m, bb[k], k += m]; bb[k] = True; k]];
a[n_] := b[n+2] b[n+1]/b[n];
Array[a, 100] (* Jean-François Alcover, Nov 12 2020, after Alois P. Heinz *)
import Data.List (delete)
a075075 n = a075075_list !! (n-1)
a075075_list = 1 : 2 : f 1 2 [3..] where
f z z' xs = g xs where g (u:us) =
if (z * u) `mod` z' > 0 then g us else u : f z' u (delete u xs)
-- Reinhard Zumkeller, Dec 19 2012
N = 10^6;
Avail = ones(1,N);
A = zeros(1,N);
A(1) = 1; A(2) = 2;
Avail([1,2]) = 0;
for n=3:N
q = round(A(n-1)/gcd(A(n-1),A(n-2)));
b = find(Avail(q*[1:floor(N/q)]),1,'first');
if numel(b) == 0
break
end
A(n) = q*b;
Avail(A(n)) = 0;
end
A = A(1:n-1); % Robert Israel, Jul 10 2015
b:= proc(n) option remember; false end: a:= proc(n) option remember; local k, m; if n<3 then b(n):= true; n else m:= denom(a(n-2) /a(n-1)); for k from m by m while b(k) do od; b(k):= true; k fi end: seq(a(n), n=1..100); # Alois P. Heinz, May 16 2009
f[s_List] := Block[{m = Numerator[ s[[ -1]]/s[[ -2]] ]}, k = m; While[ MemberQ[s, k], k += m]; Append[s, k]]; Nest[f, {1, 2}, 70] (* Robert G. Wilson v, May 20 2009 *)
from math import gcd A075075_list, l1, l2, m, b = [1,2], 2, 1, 2, {1,2} for _ in range(10**3): i = m while True: if not i in b: A075075_list.append(i) l1, l2, m = i, l1, i//gcd(l1,i) b.add(i) break i += m # Chai Wah Wu, Dec 09 2014
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