A305213 a(n) is the smallest nonnegative integer whose first n binary digits coincide with its first n decimal digits.

0, 10, 110, 10010, 10011, 110101, 10011000, 10011000, 110100011, 10010101000, 10010101001, 101111000101, 10010001101010, 10010001101010, 101101111110011, 1111110010100011, 10001110000111111, 101100111001011100, 1111011010110001101, 10001010110010101011, 101011110011100111110

Offset

1,2

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..150

Example

10011 expressed in binary is 10011100011011_2. It is the smallest number for which the first 5 digits coincide, so a(5)=10011.

Prog

(Python)
RDXHI=10
RDXLO=2
def solvematch(startHi, startLo, digleft, powHi, powLo):
    global RDXHI, RDXLO
    if digleft<=0:
        return startHi
    if powHi<0 or powLo<0:
        return None
    startd = 1 if startHi==0 else 0
    for d in range(startd, RDXLO):
        bh=startHi + d * RDXHI**powHi
        bl=startLo + d * RDXLO**powLo
        if bh<(bl+RDXLO**powLo) and bl<(bh+RDXHI**powHi):
            res=solvematch(bh, bl, digleft-1, powHi-1, powLo-1)
            if res!=None:
                return res
    return None
def A305213(n):
    if n<=1:
        return 0 # Special case: leading and only digit is 0
    d_hi =n-1
    sol=None
    while sol==None:
        d_lo=d_hi
        while(RDXLO**d_lo < 2* RDXHI**d_hi):
            res=solvematch(0, 0, n, d_hi, d_lo)
            if res!=None:
                sol = min(sol, res) if sol else res
            d_lo+=1
        d_hi+=1
    return sol

Crossrefs

Not a subsequence of A181929 (consider 10010).

Sequence in context: A337351 A146753 A297500 * A181929 A339713 A020767

Adjacent sequences: A305210 A305211 A305212 * A305214 A305215 A305216

Keyword

nonn,base

Author

Bert Dobbelaere, May 27 2018

Status

approved