A109834 - OEIS

%I #14 Nov 03 2023 12:00:21

%S 1,2,6,24,120,720,5040,40320,362880,362880,362880,362880,362880,

%T 362880,362880,362880,362880,362880,362880,725760,1451520,2903040,

%U 5806080,11612160,23224320,46448640,92897280,185794560,371589120,1114767360

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

%C 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).

%H G. C. Greubel, <a href="/A109834/b109834.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Cobham, <a href="http://dx.doi.org/10.1007/BF01706087">Uniform Tag Sequences</a>, Mathematical Systems Theory, 6 (1972), 164-192.

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

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

%F 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.

%e 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.

%t Table[Product[Floor[k/10^(Floor[Log10[k]])], {k,1,n}], {n,1,50}] (* _G. C. Greubel_, May 16 2017 *)

%t FoldList[Times,Table[IntegerDigits[n][[1]],{n,30}]] (* _Harvey P. Dale_, Aug 07 2019 *)

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

%K base,easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Aug 31 2005