A048340 a(n) in base 16 is a repdigit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 273, 546, 819, 1092, 1365, 1638, 1911, 2184, 2457, 2730, 3003, 3276, 3549, 3822, 4095, 4369, 8738, 13107, 17476, 21845, 26214, 30583

Offset: 0

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• base
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1500
• Eric Weisstein's World of Mathematics, Repdigit

Crossrefs

Cf. A010785, A033029, A028987, A028988.

Programs

Mathematica

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 16], {n, 0, 50}, {d, 15}]]] (* Vincenzo Librandi, Feb 06 2014 *)

Python

A048340_list = [0] + [int(d*l,16) for l in range(1,10) for d in '123456789abcdef'] # Chai Wah Wu, May 30 2016

Formula

From Chai Wah Wu, May 30 2016: (Start)

a(n) = 17*a(n-15) - 16*a(n-30) for n > 29.

x*(15*x^14 + 14*x^13 + 13*x^12 + 12*x^11 + 11*x^10 + 10*x^9 + 9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(16*x^30 - 17*x^15 + 1).

(End)

a(n) = (n - 15*floor((n-1)/15))*(16^floor((n+14)/15) - 1)/15. - Ilya Gutkovskiy, May 30 2016