A333552 -id:A333552 - cp's OEIS frontend

A333549 Consider the list (A333552) of numbers m defined by property that when the Recamán term A005132(m) is being computed, we are unable to subtract m from A005132(m-1) because, although A003132(m-1) >= m, the result of the subtraction, A005132(m-1)-m, is already in A005132; sequence gives the successive values of A005132(m-1)-m.

0, 1, 6, 3, 0, 7, 24, 21, 13, 45, 42, 0, 25, 90, 87, 84, 81, 78, 63, 163, 160, 157, 154, 39, 151, 264, 261, 17, 14, 11, 8, 3, 135, 114, 285, 282, 279, 276, 273, 270, 81, 78, 265, 453, 63, 46, 269, 266, 263, 260, 257, 18, 15, 12, 9, 6, 3, 0, 228, 514, 511, 508, 505, 502, 499, 496, 493, 490, 164, 502, 499, 496

Offset: 1

N. J. A. Sloane, May 02 2020

nonn

These are the collisions that are avoided when A005132 is being constructed.

			After we have found A005132(6)=13, we attempt to subtract 7 from 13 to get a(7). However, this would give 6, which is a collision, since we already have A005132(3)=6. So 6 gets added to the current sequence.

N. J. A. Sloane, Table of n, a(n) for n = 1..22288
Index entries for sequences related to Recamán's sequence

Cf. A005132, A333552.

For records see A333550, A333551.

A333553 a(n) = A333552(A333551(n)): indices of terms in Recamán's sequence A005132 where the construction avoided a record-sized collision.

Original entry on oeis.org

3, 6, 7, 18, 19, 34, 67, 102, 115, 173, 190, 288, 453, 511, 677, 846, 986, 1230, 1305, 1349, 1715, 2066, 2422, 2870, 3870, 4139, 4599, 4649, 5027, 5899, 7676, 8220, 8742, 9558, 11542, 13144, 13511, 15541, 16001, 16281, 16685, 17199, 18279, 19463, 21267, 23375, 23976, 24260, 24381, 24398, 24399, 55506, 68108, 75688

Offset: 1

N. J. A. Sloane, May 03 2020, following a suggestion from Paul Zimmermann

nonn

			After we have found A005132(6)=13, we attempt to subtract 7 from 13 to get a(7). However, this would give 6, which is a collision, since we already have A005132(3)=6. Furthermore, 6 is larger than any collision we have so far avoided. So 7 (the index of the term of A005132 that we were constructing), gets added to the current sequence (it is a(3)).

Rémy Sigrist, Table of n, a(n) for n = 1..365
Index entries for sequences related to Recamán's sequence
Rémy Sigrist, C++ program for A333553

Cf. A005132, A333548, A333549, A333550, A333551, A333552.

A187922 Positions k of addition steps in Recamán's sequence where A005132(k-1)-k = A005132(m) for some 0 < m < k.

Original entry on oeis.org

6, 7, 9, 18, 19, 21, 33, 34, 36, 66, 67, 69, 71, 73, 75, 101, 102, 104, 106, 108, 113, 114, 115, 117, 121, 123, 125, 127, 133, 134, 172, 173, 175, 177, 179, 181, 183, 186, 188, 189, 190, 194, 224, 225, 227, 229, 231, 233, 236, 238, 240, 242, 244, 246, 287, 288, 290, 292, 294, 296, 298, 300, 302, 304, 339, 340, 342, 344, 346, 348, 350

Offset: 1

Reinhard Zumkeller, Mar 17 2011

nonn

Subsequence of A057165; A005132(a(n)-1) - a(n) = A005132(A187943(n));
A005132(a(n)) = A005132(a(n)-1) + a(n);
See A187921 for the other positions of addition steps in A005132.

			a(5) = 19: A005132(19-1) = 43 and 43-19>0, but the term 24=43-19 is already in A005132, therefore A005132(19)=43+19=62; A187943(5)=15 and A005132(15)=24.

Rémy Sigrist, Table of n, a(n) for n = 1..25000
Rémy Sigrist, C++ program for A187943
Index entries for sequences related to Recamán's sequence

Cf. A005132, A057165, A187921, A187943, A333548, A333552.

import Data.Set (Set, singleton, member, insert)
a187922 n = a187922_list !! (n-1)
a187922_list = r (singleton 0) 1 0 where
   r :: Set Integer -> Integer -> Integer -> [Integer]
   r s n x | x <= n           = r (insert (x+n) s) (n+1) (x+n)
           | (x-n) `member` s = n : r (insert (x+n) s) (n+1) (x+n)
           | otherwise        = r (insert (x-n) s) (n+1) (x-n)
(C++) See Links section.

Added condition "0 < m" to definition. See A333552. - N. J. A. Sloane, May 04 2020

A334494 Positions k of addition steps in Recamán's sequence A005132 where A005132(k-1)

Original entry on oeis.org

1, 2, 5, 13, 15, 17, 24, 26, 28, 30, 32, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 112, 130, 132, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 197, 199, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 250

Offset: 1

N. J. A. Sloane, May 04 2020

nonn

This is A187921 with the terms in A333548 removed. (The difference between A187921 and the present sequence is explained by the fact that originally A005132 began at 1 rather than 0.)

Cf. A005132, A187921, A187922, A333548, A333552.

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A333553 a(n) = A333552(A333551(n)): indices of terms in Recamán's sequence A005132 where the construction avoided a record-sized collision.

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A187922 Positions k of addition steps in Recamán's sequence where A005132(k-1)-k = A005132(m) for some 0 < m < k.

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A334494 Positions k of addition steps in Recamán's sequence A005132 where A005132(k-1)

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