A244959 Smallest positive multiple of n whose base 8 representation contains only 0's and 1's.
1, 8, 9, 8, 65, 72, 299593, 8, 9, 520, 4169, 72, 65, 2396744, 585, 64, 4097, 72, 513, 520, 17044041, 33352, 33281, 72, 266825, 520, 513, 2396744, 266249, 4680, 4681, 64, 32769, 32776, 16814665, 72, 262145, 4104, 585, 520, 32841, 136352328, 36937, 33352, 585
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Ed Pegg Jr., 'Binary' Puzzle
- Eric M. Schmidt, Sage code to compute this sequence (use b=8)
- Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.
Programs
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Mathematica
Module[{nn=10,b8},b8=Rest[FromDigits[#,8]&/@Tuples[{0,1},nn]];Table[SelectFirst[ b8,Mod[#,n]==0&],{n,100}]] (* Harvey P. Dale, Feb 03 2024 *) -
Python
def A244959(n): if n > 0: for i in range(1,2**n): x = int(bin(i)[2:],8) if not x % n: return x return 0 # Chai Wah Wu, Dec 30 2014
Extensions
Data corrected, offset corrected, and b-file replaced by Harvey P. Dale, Feb 03 2024