2, 3, 10, 30, 104, 312, 1040,.. Blue sequence

Blue sequence, just because it is made of the biggest n-blockers. Among the blockers of the R-sequence, we have:

2, 3, 9, 10, 27, 28, 30, 81, 84, 88, 90, 100, 104, 243, 252, 264, 270, 272, 280, 300, 304, 312, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912,
928, 936, 992, 1000, 1040, 2187, 2208, 2268, 2352, 2368, 2376, 2430, 2448, 2464, 2520, 2624

Then, we take it by n-blockers (blockers with n divisors), thus:

2,

3,

9, 10,

27, 28, 30,

81, 84, 88, 90, 100, 104,

243, 252, 264, 270, 272, 280, 300, 304, 312,

729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912,  928, 936, 992, 1000, 1040,

1040, 2187, 2208, 2268, 2352, 2368, 2376, 2430, 2448, 2464, 2520, 2624,.. (don’t have more numbers)

Then, we take the smallest of the blockers, so we have the B-sequence: 2, 3, 10, 30, 104, 312, 1040,.. . We know that smallest of n-blockers is of form 3^x, we need the last one to estimate the amount of the blockers. 30/10=3,104/30=3.46666…7, 312/104=3, 1040/312=3,333…

Can we find the limit of the B-sequence? Were it \pi, that’d be beautiful indeed.

And also, as a side note, think of p_1p_2+p_2p_3+..+p_{n-1}p_{n}, with p_i arbitrary distinct primes. I stretched those nums on big data hyperplane and wandered around with swarm particles and random walk to learn if I could extract features. But this automated approach seems not to be enough intelligent for this opponent. For primes we might need a totally new perspective, might be R-sequence could help. Can we connect it to the R-sequence? Can we connect it to number spectrum I described some time ago? Or maybe we could exploit some experience from (previously more) experimental sciences (Gauss would not agree, since he first got results, then connected dots) and try to think as how we could combine the model of potentially infinite number of “smallest possible” building blocks with the Aufbau principle in particle physics?

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About misha

Imagine a story that one can't believe. Hi. Life changes here. Small things only.
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