[jcexjdfy] 2,3,5-balanced smooth numbers

Among smooth numbers, numbers of the form 2^x * 3^y * 5^z seem especially aesthetically smooth, because those first 3 primes don't seem as weird as primes 7 and larger.  Which exponents (x,y,z) are nice?  We propose the following, which attempts to maintain a balance between the exponents according to the size of their bases.

Start with a positive integer N.
Let c2 be the largest power of 2 less than or equal to the given value N.
Let c3 be the largest power of 3 less than or equal to the given value N.
Let c5 be the largest power of 5 less than or equal to the given value N.
Form the product c2*c3*c5.  It is roughly O(N^3).

Below are the unique elements of the sequence formed as N grows.  We see the bakers' favorite number 12 and Babylonians' favorite numbers 60 (not 30) and 360.

How can this sequence be computed efficiently?  What is its asymptotic growth rate?

1 2 6 12 60 120 360 720 3600 10800 21600 43200 129600 648000 1296000 3888000 7776000 15552000 77760000 233280000 466560000 933120000 2799360000 13996800000 27993600000 83980800000 167961600000 839808000000 1679616000000 5038848000000 10077696000000 30233088000000 60466176000000 302330880000000 604661760000000 1813985280000000 3627970560000000 18139852800000000 36279705600000000 108839116800000000 ...

The following primes are one greater than a number on the list:

2 3 7 13 61 21601 43201 15552001 466560001 13996800001 ...

43201 is a permutation of the digits 01234.

Here is the same idea applied to 2^x * 5^y:

1 2 4 20 40 80 400 800 1600 8000 16000 32000 64000 320000 640000 1280000 6400000 12800000 25600000 128000000 256000000 512000000 1024000000 5120000000 10240000000 20480000000 102400000000 204800000000 409600000000 2048000000000 4096000000000 ...

Here is the same idea applied to 2^x * 3^y, suggesting a subset of the Pierpont primes.

1 2 6 12 24 72 144 432 864 1728 5184 10368 31104 62208 124416 373248 746496 1492992 4478976 8957952 26873856 53747712 107495424 322486272 644972544 1934917632 3869835264 7739670528 23219011584 46438023168 92876046336 278628139008 557256278016 ...