|
|
A062090
|
|
a(1) = 1, a(n) = smallest odd number that does not divide the product of all previous terms.
|
|
13
|
|
|
1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
If "a(1) = 1," is removed from the definition, the subsequent terms remain the same, since 1 is the empty product. The resulting sequence then comprises the odd terms of A050376. - Peter Munn, Nov 03 2020
|
|
LINKS
|
|
|
FORMULA
|
1 together with numbers of the form p^(2^k) where p is an odd prime and k is a nonnegative integer. [Corrected by Peter Munn, Nov 03 2020]
|
|
EXAMPLE
|
After 13 the next term is 17 (not 15) as 15 = 3*5 divides the product of all the previous terms.
|
|
MATHEMATICA
|
a = {1}; Do[b = Apply[ Times, a]; k = 1; While[ IntegerQ[b/k], k += 2]; a = Append[a, k], { n, 2, 60} ]; a
nxt[{p_, on_}]:=Module[{c=on+2}, While[Divisible[p, c], c+=2]; {p*c, c}]; NestList[ nxt, {1, 1}, 60][[All, 2]] (* Harvey P. Dale, Jul 29 2021 *)
|
|
PROG
|
(Haskell)
a062090 n = a062090_list !! (n-1)
a062090_list = f [1, 3 ..] [] where
f (x:xs) ys = g x ys where
g _ [] = x : f xs (x : ys)
g 1 _ = f xs ys
g z (v:vs) = g (z `div` gcd z v) vs
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|