A165804 Numbers of the form i*8^j-1 (i=1..7, j >= 0).

0, 1, 2, 3, 4, 5, 6, 7, 15, 23, 31, 39, 47, 55, 63, 127, 191, 255, 319, 383, 447, 511, 1023, 1535, 2047, 2559, 3071, 3583, 4095, 8191, 12287, 16383, 20479, 24575, 28671, 32767, 65535, 98303, 131071, 163839, 196607, 229375, 262143, 524287, 786431, 1048575, 1310719, 1572863, 1835007, 2097151

Offset: 1

Author

N. J. A. Sloane, Jan 25 2011

Keywords

• nonn
• easy

Comments

Numbers whose sum of digits in base 8 sets a new record. - Harvey P. Dale, Jan 10 2024

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,8,-8).

Crossrefs

Smallest number whose base b sum of digits is n: A000225 (b=2), A062318 (b=3), A180516 (b=4), A181287 (b=5), A181288 (b=6), A181303 (b=7), this sequence (b=8), A140576 (b=9), A051885 (b=10). - Jason Kimberley, Nov 02 2011

Programs

Mathematica

Sort[Flatten[Table[i 8^j-1,{i,1,7},{j,0,7}]]]  (* Harvey P. Dale, Feb 03 2011 *)

Formula

G.f.: x^2*(x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)*(8*x^7-1)). [Colin Barker, Feb 01 2013]