A301652 Triangle read by rows: row n gives the digits of n in factorial base in reversed order.

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

Links

Seiichi Manyama, Rows n = 0..2000, flattened

Wikipedia, Factorial number system.

Index entries for sequences related to factorial base representation.

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

Adjacent sequences: A301649 A301650 A301651 * A301653 A301654 A301655

Keyword

nonn,tabf,base

Author

Seiichi Manyama, Mar 25 2018

Status

approved