A139389 Powers of ten in factorial base.

1, 120, 4020, 121220, 1651220, 23551220, 266251220, 2750051220, 25551151220, 210564451220

Offset

0,2

Comments

Next term has a "ten" digit.

Also called factoradix.

With hexadecimal extended to use the whole alphabet, the sequence continues: 17a5726651220, 12092315551220, b6781182251220, 799b90920051220, 4c71069221151220, 2dcaa584234451220, 1a1f264b9386651220, fb2797aa5975551220, 8437c58494852251220, 423g9bad8a4580051220, 1k213c54aa81881151220

10^48 needs a "36" digit. We can say with high probability that 10^64 is the last value that can be written without needing any digits larger than 35 (checked up to 10^1400, where it is vanishingly unlikely).

Links

Table of n, a(n) for n=0..9.

Jonathan Wellons, The Factorial Base, 2008.

Index entries for sequences related to factorial base representation.

Formula

a(n) = A007623(A011557(n)). - Amiram Eldar, Feb 21 2024

Example

10000 = 1 * 7! + 6 * 6! + 5 * 5! + 1 * 4! + 2 * 3! + 2 * 2! + 0 * 1!. Hence 10000 is 1651220 in factoradix.

Mathematica

a[n_] := Module[{k = 10^n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; FromDigits[Reverse @ s]]; Array[a, 10, 0] (* Amiram Eldar, Feb 21 2024 *)

Crossrefs

Cf. A007623, A011557.

Sequence in context: A282612 A231136 A222003 * A166596 A000514 A179060

Adjacent sequences: A139386 A139387 A139388 * A139390 A139391 A139392

Keyword

base,easy,nonn

Author

Jonathan Wellons (wellons(AT)gmail.com), Jun 08 2008

Status

approved