A185008 -id:A185008 - cp's OEIS frontend

A218643 Array, by antidiagonals, A(n,k) = next number that is the product of exactly k primes (not necessarily distinct) after 10*n.

2, 4, 11, 8, 14, 23, 16, 12, 21, 31, 32, 16, 27, 33, 41, 64, 32, 24, 42, 46, 53, 128, 64, 32, 36, 42, 51, 61, 256, 128, 64, 32, 54, 52, 62, 71, 512, 256, 128, 64, 48, 54, 63, 74, 83, 1024, 512, 256, 128, 64, 72, 81, 75, 82, 97, 2048, 1024, 512, 256, 128, 64, 72, 81, 92, 91, 101, 4096, 2048, 1024, 512, 256, 128, 64, 72, 81, 92, 106, 113, 8192, 4096, 2048, 1024, 512, 256, 128, 96, 108, 100, 102, 111, 127

Offset: 1

Jonathan Vos Post, Nov 03 2012

			Table begins:
========================================================
...|n=0|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=7|n=9|n=10|
k=1|.2.|.11|.23|.31|.41|.53|.61|.71|.83|.97|.101|A218255
k=2|.4.|.14|.21|.33|.46|.51|.62|.74|.82|.91|.106|A185008
k=3|.8.|.12|.27|.42|.42|.52|.63|.75|.92|.92|.102|
k=4|16.|.16|.24|.36|.54|.54|.81|.81|.81|100|.104|
k=5|32.|.32|.32|.32|.48|.72|.72|.72|108|108|.108|
k=6|64.|.64|.64|.64|.64|.64|.64|.96|.96|.96|.144|
========================================================

Cf. A008592, A218255, A185008.

A218643 := proc(n,k)
    local a;
    for a from 10*n+1 do
        if numtheory[bigomega](a) = k then
            return a;
        end if;
    end do:
end proc:
for d from 1 to 13 do
    for n from 0 to d-1 do
        printf("%d,",A218643(n,d-n)) ;
    end do:
end do: # R. J. Mathar, Nov 07 2012

A218558 Next number that is the product of exactly three (not necessarily distinct) primes, after 10*n.

Original entry on oeis.org

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, 310, 316, 322, 332, 343, 354, 363, 374, 385, 399, 402, 412, 423, 434, 442, 452, 465, 474, 483, 494, 506

Offset: 1

Jonathan Vos Post, Nov 02 2012

This is to "triprimes" A014612 as A185008 is to semiprimes A001358, and as A218255 is to primes A000040.

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

			a(0) = 8, the first number that is the product of exactly three (not necessarily distinct) primes.
a(1) = 12 = 2^2 * 3, which is >10*1=10.
a(3) = 42 even though 30 = 2*3*5 is a "triprime" because we use ">" rather that ">=" in the definition.

Cf. A008592, A014612, A218255, A185008.

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

a(n) = MIN[k in A014612 and k > 10*n = A008592(n)].

Offset corrected by Charles R Greathouse IV, Aug 30 2017

cp's OEIS Frontend

A218643 Array, by antidiagonals, A(n,k) = next number that is the product of exactly k primes (not necessarily distinct) after 10*n.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

A218558 Next number that is the product of exactly three (not necessarily distinct) primes, after 10*n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

Extensions