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A244912 Sum of leading digit in representations of n in bases 2,3,...,n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A118944 A132988 A342760 * A249745 A114956 A039256

Adjacent sequences:  A244909 A244910 A244911 * A244913 A244914 A244915

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Jul 08 2014

STATUS

approved

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Last modified September 22 05:11 EDT 2021. Contains 347605 sequences. (Running on oeis4.)