

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
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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 !! (n1)
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



