A344104 a(0) = 10; for n > 0, a(n) is a(n-1) multiplied by the number of 0's so far in the sequence.

10, 10, 20, 60, 240, 1200, 8400, 75600, 831600, 10810800, 183783600, 3491888400, 73329656400, 1686582097200, 43851134527200, 1227831766761600, 36834953002848000, 1289223355099680000, 51568934203987200000, 2372170973383411200000, 123352890615937382400000

Offset

0,1

Comments

This sequence is the multiplicative counterpart to A130232, but the initial term 0 is replaced with 10 (0 obviously results in A000004). The data demonstrates that the number of 0's grows rapidly as a(n) increases, because each term is a multiple of 10, thus adding at least one 0 to successive terms.

Links

Table of n, a(n) for n=0..20.

Formula

a(n+1) = a(n)*#_0[a(n)...a(0)], where #_0(n) is the number of 0's in n.

Example

To calculate a(5), multiply a(4)=240 by the number of 0's present in itself and previous terms, of which there are 5, thus yielding 1200.
a(6) is 1200 multiplied by 7, which is the number of 0's present so far, thus giving 8400.

Mathematica

a[0]=10; a[n_]:=a[n]=a[n-1]Count[Flatten[IntegerDigits/@Array[a, n, 0]], 0]; Array[a, 20, 0] (* Giorgos Kalogeropoulos, May 09 2021 *)

Prog

(Python)
A344104_list, c = [10], 1
for _ in range(20):
    A344104_list.append(A344104_list[-1]*c)
    c += str(A344104_list[-1]).count('0') # Chai Wah Wu, Jun 06 2021

Crossrefs

Cf. A130224, A130232.

Sequence in context: A332874 A076817 A324494 * A200984 A361037 A299576

Adjacent sequences: A344101 A344102 A344103 * A344105 A344106 A344107

Keyword

base,nonn

Author

Jamie Robert Creasey, May 09 2021

Status

approved