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A301652
Triangle read by rows: row n gives the digits of n in factorial base in reversed order.
2
0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 0, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 1, 2, 2, 0, 0, 3, 1, 0, 3, 0, 1, 3, 1, 1, 3, 0, 2, 3, 1, 2, 3, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 0, 1, 1
OFFSET
0,8
COMMENTS
Row n gives exponents for successive primes 2, 3, 5, 7, 11, etc., in the prime factorization of A276076(n). - Antti Karttunen, Mar 11 2024
FORMULA
T(n,k) = floor(n/k!) mod k+1. - Tom Edgar, Aug 15 2018
EXAMPLE
n | 1 2 6
---+---------
0 | 0;
1 | 1;
2 | 0, 1;
3 | 1, 1;
4 | 0, 2;
5 | 1, 2;
6 | 0, 0, 1;
7 | 1, 0, 1;
8 | 0, 1, 1;
9 | 1, 1, 1;
10 | 0, 2, 1;
11 | 1, 2, 1;
12 | 0, 0, 2;
13 | 1, 0, 2;
14 | 0, 1, 2;
15 | 1, 1, 2;
16 | 0, 2, 2;
17 | 1, 2, 2;
18 | 0, 0, 3;
19 | 1, 0, 3;
MATHEMATICA
row[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, AppendTo[s, r]; m++]; s]; row[0] = {0}; Array[row, 31, 0] // Flatten (* Amiram Eldar, Mar 11 2024 *)
PROG
(Sage) terms=25; print([0]+[x for sublist in [[floor(n/factorial(i))%(i+1) for i in [k for k in [1..n] if factorial(k)<=n]] for n in [1..terms]] for x in sublist]) # Tom Edgar, Aug 15 2018
CROSSREFS
Triangle A108731 with rows reversed.
Cf. A007623, A034968 (row sums), A208575 (row products), A227153 (products of nonzero terms on row n), A276076, A301593.
Sequence in context: A245818 A161491 A332998 * A030203 A208978 A333451
KEYWORD
nonn,tabf,base
AUTHOR
Seiichi Manyama, Mar 25 2018
STATUS
approved