A327737 a(n) is the sum of the lengths of the base-b expansions of n for all b with 1 <= b <= n.

1, 4, 7, 11, 14, 17, 20, 24, 28, 31, 34, 37, 40, 43, 46, 51, 54, 57, 60, 63, 66, 69, 72, 75, 79, 82, 86, 89, 92, 95, 98, 102, 105, 108, 111, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Formula

a(n) = A043000(n) + n. - A.H.M. Smeets, Sep 23 2019

Example

a(5) = 14 because 5 has the following representations in bases 1 to 5: 11111, 101, 12, 11, 10 giving a total length of 5+3+2+2+2 = 14.
a(12) = 37 because 12 in bases 1 through 12 is 1...1 (12 1's), 1100, 110, and for bases 4 through 12 we get a 2-digit number, for a total length of 12+4+3+9*2 = 37. - N. J. A. Sloane, Sep 23 2019

Prog

(Go)
package main
import (
    "fmt"
    "strconv"
)
func main() {
    // Due to limitations in strconv, this will only work for the first 36 terms
    for i := 1; i <= 36; i++ {
        count := i
        for base := 2; base <= i; base++ {
            count += len(strconv.FormatInt(int64(i), base))
        }
        fmt.Printf("%d, ", count)
    }
}
(PARI) a(n) = my(i=n); for(b=2, n, i+=#digits(n, b)); i \\ Felix Fröhlich, Sep 23 2019
(Python)
def count(n, b):
    c = 0
    while n > 0:
        n, c = n//b, c+1
    return c
n = 0
while n < 60:
    n = n+1
    a, b = n, 1
    while b < n:
        b = b+1
        a = a + count(n, b)
    print(n, a) # A.H.M. Smeets, Sep 23 2019

Crossrefs

Cf. A043000.

Sequence in context: A310724 A212447 A172513 * A081834 A078309 A195171

Adjacent sequences: A327734 A327735 A327736 * A327738 A327739 A327740

Keyword

nonn,base

Author

Steve Engledow, Sep 23 2019

Extensions

More terms from Felix Fröhlich, Sep 23 2019

Status

approved