A244912 Sum of leading digit in representations of n in bases 2,3,...,n.

1, 2, 3, 4, 6, 7, 9, 9, 11, 12, 15, 16, 18, 20, 20, 21, 25, 26, 29, 31, 33, 34, 38, 36, 38, 39, 42, 43, 47, 48, 52, 54, 56, 58, 58, 59, 61, 63, 67, 68, 72, 73, 76, 79, 81, 82, 88, 84, 88, 90, 93, 94, 99, 101, 105, 107, 109, 110, 116, 117, 119, 122, 117, 119, 123

Offset

2,2

Links

Jens Kruse Andersen, Table of n, a(n) for n = 2..1000

Example

8 in bases 2...8 is:
1000 (base 2)
22 (base 3)
20 (base 4)
13 (base 5)
12 (base 6)
11 (base 7)
10 (base 8)
The sum of first digits is 1+2+2+1+1+1+1 = 9, so a(8)=9.

Mathematica

f[n_] := Sum[ IntegerDigits[n, k][[1]], {k, 2, n}]; Array[f, 70, 2] (* Robert G. Wilson v, Aug 02 2014 *)

Prog

(Python)
import math
def modlg(a, b):
....return a // b**int(math.log(a, b))
for n in range(1, 77):
....s=0
....for k in range(2, n+1):
........s += modlg(n, k)
....print str(s)+', ',
(PARI) a(n) = sum(i=2, n, digits(n, i)[1]); \\ Michel Marcus, Jul 17 2014

Crossrefs

Cf. A004125 (sum of last digits), A043306 (sum of all digits).

Sequence in context: A132988 A363997 A342760 * A249745 A114956 A039256

Adjacent sequences: A244909 A244910 A244911 * A244913 A244914 A244915

Keyword

nonn,base

Author

Alex Ratushnyak, Jul 08 2014

Status

approved