The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A278236

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A278236

Filter-sequence for factorial base (digit values): least number with the same prime signature as A276076(n).
(history; published version)

#41 by Michel Marcus at Wed Feb 07 01:18:57 EST 2024

STATUS

reviewed

approved

#40 by Joerg Arndt at Wed Feb 07 00:41:18 EST 2024

STATUS

proposed

reviewed

#39 by Amiram Eldar at Wed Feb 07 00:24:24 EST 2024

STATUS

editing

proposed

#38 by Amiram Eldar at Wed Feb 07 00:16:59 EST 2024

LINKS

<a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

<a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.

MATHEMATICA

a[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; s = ReverseSort[s]; Times @@ (Prime[Range[Length[s]]] ^ s)]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2024 *)

STATUS

approved

editing

#37 by OEIS Server at Sat Nov 19 08:29:30 EST 2016

LINKS

Antti Karttunen, <a href="/A278236/b278236_1.txt">Table of n, a(n) for n = 0..40320</a>

#36 by N. J. A. Sloane at Sat Nov 19 08:29:30 EST 2016

STATUS

proposed

approved

Discussion

Sat Nov 19

08:29

OEIS Server: Installed new b-file as b278236.txt.  Old b-file is now b278236_1.txt.

#35 by Jon E. Schoenfield at Fri Nov 18 23:28:04 EST 2016

STATUS

editing

proposed

#34 by Jon E. Schoenfield at Fri Nov 18 23:28:01 EST 2016

COMMENTS

Any such sequence should match where the result is computed from the nonzero digits (that may also be > 9) in the factorial base representation of n, but does not depend on their order. Some of these are listed on the last line of the Crossrefs- section.

STATUS

proposed

editing

#33 by Antti Karttunen at Fri Nov 18 18:03:24 EST 2016

STATUS

editing

proposed

#32 by Antti Karttunen at Fri Nov 18 16:52:48 EST 2016

NAME

Filter-sequence for factorial base (digit values): least number with the same prime signature as A276076(n).

COMMENTS

Note that as A275735 is present in that list it means that the sequences matching to its sentinel filter-sequence A278235 form a subset of the sequences matching to this sequence. Also, for A275735 there is a stronger condition that for any i, j: a(i) = a(j) <=> A275735(i) = A275735(j), which if true, would imply that there is an injective function f such that f(A275735(n)) = A278236(n), and indeed, this function seems to be A181821.

CROSSREFS

Sequences that partition N into same or coarser equivalence classes: A275735 (<=>), A034968, A060130, A227153, A227154, A246359, A257079, A257511, A257679, A257694, A257695, A257696, A264990, A275729, A275735, A275806, A275948, A275964, A278235.

Discussion

Fri Nov 18

17:31

Antti Karttunen: PLEASE, do not shorten any of these filtering-sequences (unless absolutely must!). I have on purpose included enough terms to fill up to about 360 characters (which will nicely show as four full lines when the entry is shown to the user), so that less false positives will be generated when an automatic matching program is run with this sequence.