login
A109834
Startorial numbers: product of initial digits of integers 1 through n.
2
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
1,2
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).
LINKS
A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.
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.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Aug 31 2005
STATUS
approved