A109834 Startorial numbers: product of initial digits of integers 1 through n.

1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 725760, 1451520, 2903040, 5806080, 11612160, 23224320, 46448640, 92897280, 185794560, 371589120, 1114767360

Offset: 1

Author

Jonathan Vos Post, Aug 31 2005

Keywords

• base
• easy
• nonn

Comments

This is a base 10 sequence; the equivalent exists for other bases. For base 1 and base 2, this gives the all-one sequence (A000012).

Examples

			a(30) = 1*2*3*4*5*6*7*8*9*1*1*1*1*1*1*1*1*1*1*2*2*2*2*2*2*2*2*2*2*3 = 1114767360.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.

Crossrefs

Cf. A000030, A000040, A001221, A001222, A112264, A112266.

Programs

Mathematica

Table[Product[Floor[k/10^(Floor[Log10[k]])], {k,1,n}], {n,1,50}] (* G. C. Greubel, May 16 2017 *)
FoldList[Times,Table[IntegerDigits[n][[1]],{n,30}]] (* Harvey P. Dale, Aug 07 2019 *)

Formula

a(n) = Product_{i = 1..n} A000030(i).

a(n+1) = a(n) * InitialDigitOf(n).

a(n) = Product_{i = 1..n} floor(i / 10^(floor(log_10(i)))) where log_10(i) is the logarithm of i in base 10.