

A309096


Increasing positive integers with prime factorization exponents all appearing earlier in the sequence.


0



1, 2, 4, 6, 12, 16, 18, 30, 36, 48, 60, 64, 90, 144, 150, 162, 180, 192, 210, 240, 300, 324, 420, 450, 576, 630, 720, 810, 900, 960, 1050, 1200, 1260, 1296, 1458, 1470, 1620, 1680, 2100, 2310, 2880, 2916, 2940, 3150, 3600, 3750, 4050, 4096, 4410, 4620, 4800
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..51.


FORMULA

a(1) = 1; a(n) = least positive integer x > a(n1) where the exponents e in the prime factorization of x are in a(1..n1).


EXAMPLE

a(2) = 2, since 2 = 2^1 and all {1} are in a(1..1) = [1].
a(3) != 3, since 3 = 2^0 * 3^1 and not all {0,1} are in a(1..2) = [1,2].
a(3) = 4, since 4 = 2^2 and all {2} are in a(1..2) = [1,2].
a(4) != 5, since 5 = 2^0 * 3^0 * 5^1 and not all {0,1} are in a(1..3) = [1,2,4].
a(4) = 6, since 6 = 2^1 * 3^1 and all {1} are in a(1..3) = [1,2,4].


PROG

(Haskell)
wheelSeeds = [2, 3, 5, 7, 11, 13]
wheelOffsets = filter (\c > all (\s > mod c s /= 0) wheelSeeds) [1..product wheelSeeds]
restOfWheel = (concat (map (replicate (length wheelOffsets)) (map (* (product wheelSeeds)) [1..])))
wheel = wheelSeeds ++ (tail wheelOffsets) ++ (zipWith (+) (cycle wheelOffsets) restOfWheel)
isPrime n = and [n > 1, all (\c > mod n c /= 0) (takeWhile (\c > c * c <= n) wheel)]
primes = filter isPrime wheel
exponents bases acc n =
if (n == 1)
then (dropWhile (== 0) acc)
else if (mod n (head bases) == 0)
then (exponents bases (((head acc) + 1) : (tail acc)) (div n (head bases)))
else (exponents (tail bases) (0 : acc) n)
a = filter (\n > all (\e > elem e (takeWhile (<= e) a)) (exponents primes [0] n)) [1..]


CROSSREFS

Sequence in context: A255001 A050584 A260698 * A019280 A090748 A188047
Adjacent sequences: A309093 A309094 A309095 * A309097 A309098 A309099


KEYWORD

nonn


AUTHOR

Chris Murray, Jul 12 2019


STATUS

approved



