OFFSET
1,2
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
KEYWORD
nonn,base
AUTHOR
Steve Engledow, Sep 23 2019
EXTENSIONS
More terms from Felix Fröhlich, Sep 23 2019
STATUS
approved