The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A260084

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A260084

Infinite sequence starting with a(0)=0 such that A(a(k)) = a(k-1) for all k>=1, where A(n) = n - A037445(n).
(history; published version)

#20 by Max Alekseyev at Wed May 08 10:29:50 EDT 2024

STATUS

editing

approved

#19 by Max Alekseyev at Wed May 08 10:29:39 EDT 2024

COMMENTS

The first infinitary analog (see also A260124) of A259934 (see comment there). Using FalcaoGuba's method (2015) one can prove that such an infinite sequence exists.

STATUS

approved

editing

#18 by N. J. A. Sloane at Sun Jul 19 08:59:30 EDT 2015

STATUS

editing

approved

#17 by N. J. A. Sloane at Sun Jul 19 08:59:25 EDT 2015

CROSSREFS

Cf. A037445, A259934, A259935, A260085, A260124.

STATUS

proposed

editing

#16 by Michel Marcus at Sat Jul 18 08:09:55 EDT 2015

STATUS

editing

proposed

#15 by Michel Marcus at Sat Jul 18 08:09:42 EDT 2015

COMMENTS

A generalization. For an even m, the multipication multiplication of A260124 by 2^m and 2^(m+1) gives two infinite solutions of the system of equations for integer x_n, n>=1: A037445(x_1 + ... + x_n) = x_n/2^A005187(m), n>=1. In particular, for m=0, we obtain A260124 and A260084.

A037445(x_1 + ... + x_n) = x_n/2^A005187(m),

n>=1. In particular, for m=0, we obtain A260124 and A260084.

STATUS

proposed

editing

#14 by Vladimir Shevelev at Sat Jul 18 06:52:08 EDT 2015

STATUS

editing

proposed

#13 by Vladimir Shevelev at Sat Jul 18 06:51:57 EDT 2015

DATA

0, 2, 6, 10, 14, 18, 22, 30, 34, 42, 46, 54, 58, 62, 70, 78, 82, 90, 94, 102, 106, 114, 118, 122, 130, 138, 142, 146, 154, 158, 162, 166, 174, 182, 190, 194, 210, 214, 222, 230, 238, 242, 250, 254, 270, 274, 278, 286, 294, 298, 302, 310, 314, 330, 334, 342, 346, 354, 358, 366, 374, 390, 394, 402, 410, 418, 426, 434, 442

STATUS

proposed

editing

#12 by Vladimir Shevelev at Sat Jul 18 06:37:53 EDT 2015

STATUS

editing

proposed

#11 by Vladimir Shevelev at Sat Jul 18 06:37:43 EDT 2015

COMMENTS

A generalization. For an even m, the multipication of A260124 by 2^m and 2^(m+1) gives two infinite solutions of the system of equations for integer x_n, n>=1:

A037445(x_1 + ... + x_n) = x_n/2^A005187(m),

n>=1. In particular, for m=0, we obtain A260124 and A260084.

FORMULA

a(n) = 2 * A260124(n).

STATUS

proposed

editing