The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A355916 Variant of Inventory Sequence A342585 where indices are also counted (long version). 6
 0, 0, 2, 0, 0, 1, 4, 0, 1, 1, 1, 2, 0, 3, 6, 0, 4, 1, 2, 2, 1, 3, 2, 4, 0, 5, 8, 0, 6, 1, 5, 2, 2, 3, 3, 4, 2, 5, 2, 6, 0, 7, 10, 0, 7, 1, 9, 2, 4, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 8, 1, 9, 1, 10, 0, 11, 12, 0, 11, 1, 11, 2, 6, 3, 7, 4, 5, 5, 5, 6, 4, 7, 2, 8, 2, 9, 2, 10, 3, 11, 1, 12, 0, 13, 14, 0, 13, 1, 15, 2, 8, 3, 9, 4, 8, 5, 6, 6, 5, 7, 5, 8, 4, 9, 3, 10, 4, 11, 2, 12, 2, 13, 1, 14, 1, 15, 0, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Similar to A342585, except that when we take inventory, we write down what we are counting as a subscript on the count. So if we have found k copies of m so far, we write down k_m, and include both the k and m values when we next take inventory. More than the usual number of terms are shown, in order to match A355917. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10020 Rémy Sigrist, PARI program N. J. A. Sloane, The first eight inventories, with better alignment. EXAMPLE Initially we have no 0's, so the first inventory is 0_0. Just as in A342585, when we reach a count of zero, we take a new inventory. Now we see two 0's, so we write down 2_0, followed by 0_1, since there are no 1's. So the first two inventories are 0_0, 2_0, 0_1. Now we see four 0's, so the next inventory starts 4_0, then 1_1, 1_2, and 0_3: 4_0, 1_1, 1_2, 0_3. The first eight inventories are: 0_0, 2_0, 0_1, 4_0, 1_1, 1_2, 0_3, 6_0, 4_1, 2_2, 1_3, 2_4, 0_5, 8_0, 6_1, 5_2, 2_3, 3_4, 2_5, 2_6, 0_7, 10_0, 7_1, 9_2, 4_3, 5_4, 4_5, 3_6, 2_7, 1_8, 1_9, 1_10, 0_11, 12_0, 11_1, 11_2, 6_3, 7_4, 5_5, 5_6, 4_7, 2_8, 2_9, 2_10, 3_11, 1_12, 0_13, 14_0, 13_1, 15_2, 8_3, 9_4, 8_5, 6_6, 5_7, 5_8, 4_9, 3_10, 4_11, 2_12, 2_13, 1_14, 1_15, 0_16, ... The sequence is obtained by reading the inventories, with each count followed by its index: 0, 0, 2, 0, 0, 1, 4, 0, 1, 1, 1, 2, 0, 3, ... If the indices are omitted, we get the short version, A355917. A355918 lists the highest index in each inventory. MATHEMATICA nn = 9; c[_] = 0; a[1] = a[2] = 0; c[0] = 2; i = 3; Do[k = 0; While[c[k] > 0, Set[{a[i], a[i + 1]}, {c[k], k}]; c[a[i]]++; c[a[i + 1]]++; i += 2; k++]; Set[{a[i], a[i + 1]}, {c[k], k}]; c[a[i]]++; c[a[i + 1]]++; i += 2, {n, 2, nn}]; Array[a, i - 1] (* Michael De Vlieger, Sep 25 2022 *) PROG (PARI) See Links section. (Python) from collections import Counter def aupton(terms): num, alst, inventory = 0, [0, 0], Counter([0, 0]) for n in range(3, 3+terms//2): c = [inventory[num], num] num = 0 if c[0] == 0 else num + 1 alst.extend(c) inventory.update(c) return alst[:terms] print(aupton(128)) # Michael S. Branicky, Sep 25 2022 CROSSREFS Cf. A342585, A355917, A355918. Sequence in context: A168511 A111146 A109077 * A309023 A353429 A137585 Adjacent sequences: A355913 A355914 A355915 * A355917 A355918 A355919 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 24 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 4 19:04 EDT 2023. Contains 365888 sequences. (Running on oeis4.)