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A064839 List the natural numbers starting a new row only with each new least prime signature (A025487). a(n) is the column position associated with n. 7
1, 1, 2, 1, 3, 1, 4, 1, 2, 2, 5, 1, 6, 3, 4, 1, 7, 2, 8, 3, 5, 6, 9, 1, 3, 7, 2, 4, 10, 1, 11, 1, 8, 9, 10, 1, 12, 11, 12, 2, 13, 2, 14, 5, 6, 13, 15, 1, 4, 7, 14, 8, 16, 3, 15, 4, 16, 17, 17, 1, 18, 18, 9, 1, 19, 3, 19, 10, 20, 4, 20, 1, 21, 21, 11, 12, 22, 5, 22, 2, 2, 23, 23, 2, 24, 25, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 2 records the primes (A000040). Rows 3 and 4 record the semiprimes (A001358). Rows 5, 6 and 9 record the 3-almost primes (A014612) etc. A058933 is a similar sequence based on k-almost primes.

The graph of this sequence is interesting for large n because it shows multiple curves, one for each prime signature. For example, the six highest curves on the graph of a(n) for n up to 10^4 are for the (1,1), (1,1,1), (1), (2,1,1), (2,1), and (1,1,1,1) prime signatures. The (1) curve dominates until n=58; the (1,1) curve dominates until n=1279786, when the (1,1,1) curve intersects the (1,1) curve. Each {1,1,...,1) curve dominates for a finite number of n.

Ordinal transform of A101296. - Antti Karttunen, May 15 2017

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

EXAMPLE

The list begins as follows:

1

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 ...

4 9 25 49 ...

6 10 14 15 21 22 26 33 34 35 38 39 46 51 ...

8 27 ...

12 18 20 28 44 45 50 52 ...

16 ...

Note: the above array, without the initial 1, is given by A095904 (and its transpose A179216). - Antti Karttunen, May 15 2017

CROSSREFS

Cf. A000040, A001358, A014612, A025487, A046523, A058933, A101296.

Cf. also arrays A095904, A179216.

Sequence in context: A057499 A241919 A286469 * A255810 A210256 A229944

Adjacent sequences:  A064836 A064837 A064838 * A064840 A064841 A064842

KEYWORD

easy,nice,nonn

AUTHOR

Alford Arnold, Oct 24 2001

EXTENSIONS

More terms from Naohiro Nomoto, Oct 31 2001

STATUS

approved

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Last modified January 22 10:32 EST 2019. Contains 319363 sequences. (Running on oeis4.)