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Revision History for A357975 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Divide all prime indices by 2, round down, and take the number with those prime indices, assuming prime(0) = 1.
(history; published version)
#14 by Michel Marcus at Sun Feb 12 17:29:44 EST 2023
STATUS

reviewed

approved

#13 by Andrew Howroyd at Sun Feb 12 16:12:47 EST 2023
STATUS

proposed

reviewed

Discussion
Sun Feb 12
16:18
Sidney Cadot: Yes, newline (ascii 10, decimal).
16:21
Sidney Cadot: A handful of OEIS entries have a similar issue. I'm fixing those as they potentially wreak havoc with automated parsing. (I know I had to adapt my parser to handle them without issue, but it violates a rather hard requirement that all main files lines should start with a directive).
16:34
Andrew Howroyd: I doubt this is ascii 10 newline. If you look at https://oeis.org/A357975/internal then there is no line break. The character is visible. If you are not pulling from  https://oeis.org/A357975/internal then from where? This is clearer in some of the other Mma examples you found. The back-end to my understanding is Unix (or Linux) which does not use a combo \r\n to break lines. Also I have not encountered this. (so my guess is that this is one of the many unicode line break chars). In any case, good to fix.
16:47
Andrew Howroyd: closer inspection of the glyph says it is lsep https://www.fileformat.info/info/unicode/char/2028/index.htm
16:58
Sidney Cadot: Had a closer look. The encoded byte sequence retrieved from the server is 0xe2 0x80 0xe8, in UTF-8. It appears that, in Pythion, this specific character is mapped immediately to a plain '\n' (0x10), which is what it looks like to me after that. My script retrieves OEIS entries using Python and inserts the string into a local SQLite3 database. So you are right. That's very useful information for me -- it means that the conversion to a Python string is lossy. I will have to think how to handle that. So while getting rid of the character is useful, my initial report was indeed incorrect as you point out.
17:07
Sidney Cadot: Last message was wrong in several ways. The sequence is 0xe2 0x80 0xa8, which indeed maps currently to '\u2028' in Python and survives storage in an SQLIte3 database and subsequent retrieval. So I will have to dig a bit deeper why my code signals it as an '\n' character. (FYI: as you may have guessed, I have written a lint-like tool for OEIS entries).
17:26
Andrew Howroyd: Python has been modernized to deal with unicode. You probably cannot stop it translating unicode line separators. (without writing/overriding some low-level binary -> text stream class). The right thing to do is to remove them - I was just curious as to what they were and now that we know we can still eliminate them.
17:28
Andrew Howroyd: (btw I'm just happily inventing the rules here - this time to your benefit.)
#12 by Sidney Cadot at Sun Feb 12 15:58:53 EST 2023
STATUS

editing

proposed

Discussion
Sun Feb 12
16:12
Andrew Howroyd: Out of interest what ASCII / Unicode char is this? Surely not newline (\n)?
#11 by Sidney Cadot at Sun Feb 12 15:57:07 EST 2023
CROSSREFS

Positions of first appearances are A297002, sorted A066207.

STATUS

approved

editing

Discussion
Sun Feb 12
15:58
Sidney Cadot: The "crossrefs" section (%Y) had a spurious newline character after the line "Positions of first appearances are A297002, sorted A066207.", and thus an empty line, violating the constraint that all lines in a main file should start with a % directive.
#10 by Michael De Vlieger at Sun Oct 23 20:46:39 EDT 2022
STATUS

proposed

approved

#9 by Gus Wiseman at Sun Oct 23 20:34:22 EDT 2022
STATUS

editing

proposed

#8 by Gus Wiseman at Sun Oct 23 20:34:20 EDT 2022
#7 by Gus Wiseman at Sun Oct 23 18:19:37 EDT 2022
FORMULA

Completely multiplicative with a(prime(2k)) = prime(k) and a(prime(2k + 1)) = prime(k). Cf. A297002.

a(prime(n)) = A109763(n - 1).

CROSSREFS

Positions of first appearances are A297002 (an inverse version), , sorted A066207.


A004526 is floor(n/2) , with an extra first zero.

Cf. A003961 mult_nextpri, A033879 2minus_sumdiv, A033880 sumdiv_minus2, A045966 mult_nextnextpri, A064988 mult_pri_p_then_to_e, A064989 mult_prevpri, `A076610 prix_pri, A215366 h_tri, A248601 what, A357975 half_prix_floor, A357977 mtf_p, A357978 mtf_q, A357979 mtf_mtf_p, A357980 mtf_pi, A357981 prix_prix_pri.

Cf. A003961, A064988, A064989, `A076610, A215366, `A248601, A357980.

#6 by Gus Wiseman at Sun Oct 23 17:36:39 EDT 2022
COMMENTS

Each n appears A000005(n) times at odd positions (infinitely many at even). To see this, write n as a product of an element of note that our transformation does not distinguish between A066207 and an element of A066208.

#5 by Gus Wiseman at Sun Oct 23 17:31:40 EDT 2022
MATHEMATICA

Table[Times@@(If[#1<=2, 1, Prime[Floor[PrimePi[#1]/2]]^#2]&@@@FactorInteger[n]), {n, 100}]