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Revision History for A218558

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A218558

Next number that is the product of exactly three (not necessarily distinct) primes, after 10*n.
(history; published version)

#12 by Charles R Greathouse IV at Wed Aug 30 03:01:37 EDT 2017

STATUS

editing

approved

#11 by Charles R Greathouse IV at Wed Aug 30 03:01:32 EDT 2017

OFFSET

0,1,1

COMMENTS

The first equal terms are a(4) = a(5) = 42. The density of numbers n such that a(n) = a(n+1) is 1. Similarly, the density of numbers n such that a(n) = a(n+1) = ... = a(n+k) is 1 for any fixed k. - Charles R Greathouse IV, Aug 30 2017

PROG

(PARI) a(n)=n*=10; while(bigomega(n++)!=3, ); n \\ Charles R Greathouse IV, Aug 30 2017

EXTENSIONS

Offset corrected by Charles R Greathouse IV, Aug 30 2017

STATUS

approved

editing

#10 by T. D. Noe at Tue Nov 13 00:49:21 EST 2012

STATUS

proposed

approved

#9 by R. J. Mathar at Wed Nov 07 14:40:08 EST 2012

STATUS

editing

proposed

Discussion

Wed Nov 07

15:20

Charles R Greathouse IV: I think the array would be better, with a(n) being replaced by a(n, 3). The array has the property that a(n, k) = a(n+1, k) for any k and almost all n.

#8 by R. J. Mathar at Wed Nov 07 14:40:03 EST 2012

KEYWORD

nonn,easy,more,changed

#7 by R. J. Mathar at Wed Nov 07 14:39:36 EST 2012

DATA

8, 12, 27, 42, 42, 52, 63, 75, 92, 92, 102, 114, 124, 138, 147, 153, 164, 171, 182, 195, 207, 212, 222, 231, 242, 255, 261, 273, 282, 292, 316, 310, 316, 322, 333, 332, 343, 354, 363, 374, 385, 399, 402, 412, 423, 434, 442, 452, 465, 474, 483, 494, 506

STATUS

proposed

editing

#6 by Jonathan Vos Post at Fri Nov 02 17:14:38 EDT 2012

STATUS

editing

proposed

Discussion

Fri Nov 02

17:28

T. D. Noe: Suggest deleting this.

Sat Nov 03

13:33

Jonathan Vos Post: The array also is useful in the supersequence of prime gaps, semiprime gaps, triprime gaps...  It has implicitly "decades without a prime", "decades without a semiprime", "decades without a triprime", where values of that row are repeated.  For example, in this seq (row 3) we have two consecutive values of 43 because there are no triprimes strictly between 30 and 40.

14:20

Jonathan Vos Post: I mean, two consecutive values of 42.  Sorry.

17:26

M. F. Hasler: If the sequence should remain, I suggest the NAME "Least number > 10^n which...."

But I'd be in favour of replacing the sequence by the mentioned square array, of which it is the 3rd row.

#5 by Jonathan Vos Post at Fri Nov 02 17:14:23 EDT 2012

DATA

8, 12, 27, 42, 42, 52, 63, 75, 92, 92, 102, 114, 124, 138, 147, 153, 164, 171, 182, 195, 207, 212, 222, 231, 242, 255, 261, 273, 282, 292, 316, 316, 322, 333, 343, 354, 363, 374, 385, 399, 402, 412, 423, 434, 442

#4 by Joerg Arndt at Fri Nov 02 13:49:36 EDT 2012

STATUS

proposed

editing

Discussion

Fri Nov 02

17:02

Jonathan Vos Post: Joerg Arndt is right, but this is merely the 3rd row of an array, of which A218255 is the 1st row (products of one prime), A185008 is the 2nd row (products of two primes), The entire array is slightly more interesting than any indiviidual row.

#3 by Jonathan Vos Post at Fri Nov 02 13:45:03 EDT 2012

STATUS

editing

proposed

Discussion

Fri Nov 02

13:49

Joerg Arndt: Frankly, to me this one seems both arbitrary and remarkably uninteresting.
Is it interesting enough to you to spend those precious two minutes to compute 3 lines worth of terms?