The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A265743

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A265743

a(n) = number of terms of A005187 needed to sum to n using the greedy algorithm.
(history; published version)

#9 by N. J. A. Sloane at Fri Dec 18 11:26:26 EST 2015

STATUS

proposed

approved

#8 by Antti Karttunen at Thu Dec 17 07:47:00 EST 2015

STATUS

editing

proposed

Discussion

Thu Dec 17

08:57

Antti Karttunen: Number of greedy carryless sums of A005187, "carryless" meaning that n = A005187(x) + A005187(y) + A005187(z) = A005187(x) XOR A005187(y) XOR A005187(z).
/// Similar construction for A003714 (Fibbinary numbers).

08:58

Antti Karttunen: @8:57: Those in my long-term todo-list.

#7 by Antti Karttunen at Thu Dec 17 07:43:54 EST 2015

CROSSREFS

Cf. also A000120, A007895, A053610, A265404, A265744, A265745.

#6 by Antti Karttunen at Thu Dec 17 07:34:12 EST 2015

LINKS

Antti Karttunen, <a href="/A265743/b265743.txt">Table of n, a(n) for n = 0..8192</a>

#5 by Antti Karttunen at Thu Dec 17 07:33:13 EST 2015

COMMENTS

a(0) = 0, because no numbers are needed to get form an empty sum, which is zero.

FORMULA

Other identities. For all n >= 1:

a(A005187(n)) = 1 and a(A055938(n)) > 1.

CROSSREFS

Cf. A005187, A055938.

#4 by Antti Karttunen at Thu Dec 17 07:00:35 EST 2015

NAME

a(n) = number of positive terms of A005187 needed to sum to n using the greedy algorithm.

COMMENTS

a(0) = 0, because no numbers are needed to get an empty sum, zero.

CROSSREFS

Cf. also A007895, A053610, A265404, A265744, A265745.

Discussion

Thu Dec 17

07:01

Antti Karttunen: I think "positive" is unnecessary qualification for these sequences because the "greedy" already excludes the unnecessary zero-summands in the sum.

#3 by Antti Karttunen at Thu Dec 17 06:47:25 EST 2015

NAME

allocated for Antti Karttunena(n) = number of positive terms of A005187 needed to sum to n using the greedy algorithm.

DATA

0, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 4, 1, 1

OFFSET

0,3

CROSSREFS

Cf. A005187.

Cf. also A007895, A265404, A265744, A265745.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Dec 17 2015

STATUS

approved

editing

#2 by Antti Karttunen at Tue Dec 15 14:12:20 EST 2015

KEYWORD

allocating

allocated

#1 by Antti Karttunen at Tue Dec 15 14:12:20 EST 2015

NAME

allocated for Antti Karttunen

KEYWORD

allocating

STATUS

approved