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A358066
Inventory sequence: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1 (see example).
3
1, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 5, 4, 6, 7, 1, 2, 3, 5, 9, 4, 6, 10, 7, 11, 8, 13, 1, 2, 3, 5, 9, 16, 4, 6, 10, 17, 7, 11, 18, 8, 13, 21, 12, 19, 1, 2, 3, 5, 9, 16, 28, 4, 6, 10, 17, 29, 7, 11, 18, 30, 8, 13, 21, 34, 12, 19, 31, 14, 22, 35, 1, 2, 3, 5, 9, 16, 28, 46, 4, 6, 10, 17, 29, 47, 7, 11, 18, 30, 48
OFFSET
1,4
EXAMPLE
At stage n >= 1 we only look at the numbers 1 up to n, and ignore numbers bigger than n.
Stage 0: start with a(1) = 1, a(2) = 1.
Stage 1: we see 1's at 1,2, so we adjoin 1,2, getting 1,1, 1,2.
Stage 2: we see 1's at 1,2,3, and 2's at 4, so we adjoin 1,2,3,4, getting 1,1,1,2, 1,2,3,4.
Stage 3: we see 1's at 1,2,3,5, 2's at 4,6 and 3's at 7, so we adjoin 1,2,3,5,4,6,7, getting 1,1,1,2,1,2,3,4, 1,2,3,5,4,6,7.
Stage 4: we see 1's at 1,2,3,5,9, 2's at 4,6,10, 3's at 7,11, 4's at 8,13, so we adjoin 1,2, ..., 8,13 and so on.
We obtain an irregular triangle by writing the results of the stages as separate rows:
1, 1,
1, 2,
1, 2, 3, 4,
1, 2, 3, 5, 4, 6, 7,
1, 2, 3, 5, 9, 4, 6, 10, 7, 11, 8, 13,
1, 2, 3, 5, 9, 16, 4, 6, 10, 17, 7, 11, 18, 8, 13, 21, 12, 19,
1, 2, 3, 5, 9, 16, 28, 4, 6, 10, 17, 29, 7, 11, 18, 30, 8, 13, 21, 34, 12, 19, 31, 14, 22, 35,
... (N. J. A. Sloane, Nov 07 2022)
PROG
(Python)
terms = [1, 1]
for i in range(1, 11):
new_terms = []
for j in range(1, i+1):
for k in range(len(terms)):
if terms[k] == j: new_terms.append(k+1)
terms.extend(new_terms)
print(terms) # Gleb Ivanov, Nov 01 2022
CROSSREFS
See A357443 for another version.
Sequence in context: A168265 A062050 A358086 * A358085 A357443 A233782
KEYWORD
nonn,tabf
AUTHOR
Ctibor O. Zizka, Oct 29 2022
STATUS
approved