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Revision History for A328099

(Underlined text is an addition; strikethrough text is a deletion.)

Showing all changes.
A328099 a(n) = min(A003415(n), A276086(n)).
(history; published version)
#9 by Susanna Cuyler at Tue Oct 08 16:26:08 EDT 2019
STATUS

proposed

approved

#8 by Jon E. Schoenfield at Mon Oct 07 21:34:00 EDT 2019
STATUS

editing

proposed

Discussion
Tue Oct 08 04:14 
Antti Karttunen: Yes, definitely better. Thanks!
#7 by Jon E. Schoenfield at Mon Oct 07 21:33:13 EDT 2019
COMMENTS

ChoosingAlways alwayschoosing the smaller onelesser of A003415(n) and A276086(n) is often a good heuristicsheuristic when trying to find the shortest path to zero. However, this doesn't always guarantee the optimal result. E.g., if we define b(0) = 0; and for n > 0, b(n) = 1+(a(n)), then we have b(8) = 8 > A327969(8) = 6, b(12) = 7 > A327969(12) = 5, and b(15) = 9 > A327969(15) = 6.

STATUS

proposed

editing

Discussion
Mon Oct 07 21:34 
Jon E. Schoenfield: Does this look okay?
#6 by Antti Karttunen at Mon Oct 07 15:15:48 EDT 2019
STATUS

editing

proposed

#5 by Antti Karttunen at Mon Oct 07 14:56:32 EDT 2019
COMMENTS

Choosing always the smaller one of A003415(n) and A276086(n) is often good heuristics when trying to find the shortest path to zero. However, this doesn't always guarantee the optimal result. E.g., if we define b(0) = 0; and for n > 0, b(n) = 1+(a(n)), then we have b(8) = 8 > A327969(8) = 6, b(12) = 7 > A327969(12) = 5, and b(15) = 9 > A327969(15) = 6.

CROSSREFS

Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A327969, A328097, A328098, A328112.

#4 by Antti Karttunen at Mon Oct 07 11:06:15 EDT 2019
LINKS

Antti Karttunen, <a href="/A328099/b328099.txt">Table of n, a(n) for n = 1..65537</a>

#3 by Antti Karttunen at Mon Oct 07 10:12:54 EDT 2019
CROSSREFS

Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A328097, A328098, A328112.

#2 by Antti Karttunen at Mon Oct 07 07:23:03 EDT 2019
NAME

allocated for Antti Karttunen

a(n) = min(A003415(n), A276086(n)).

DATA

0, 1, 1, 4, 1, 5, 1, 12, 6, 7, 1, 16, 1, 9, 8, 32, 1, 21, 1, 24, 10, 13, 1, 44, 10, 15, 27, 32, 1, 7, 1, 21, 14, 19, 12, 35, 1, 21, 16, 68, 1, 41, 1, 48, 39, 25, 1, 112, 14, 45, 20, 56, 1, 81, 16, 92, 22, 31, 1, 49, 1, 33, 51, 192, 18, 61, 1, 72, 26, 59, 1, 156, 1, 39, 55, 80, 18, 71, 1, 176, 108, 43, 1, 124, 22, 45, 32, 140, 1, 123, 20, 96, 34, 49, 24

OFFSET

1,4

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };

A328099(n) = min(A003415(n), A276086(n));

CROSSREFS

Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A328097, A328098.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Oct 07 2019

STATUS

approved

editing

#1 by Antti Karttunen at Fri Oct 04 02:09:47 EDT 2019
NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved

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Last modified August 18 19:26 EDT 2024. Contains 375273 sequences. (Running on oeis4.)