A048447 Take the first n numbers written in base 16, concatenate them, then convert from base 16 to base 10.

1, 18, 291, 4660, 74565, 1193046, 19088743, 305419896, 4886718345, 78187493530, 1250999896491, 20015998343868, 320255973501901, 5124095576030430, 81985529216486895, 20988295479420645136, 5373003642731685154833, 1375488932539311399637266, 352125166730063718307140115

Offset: 1

Author

Patrick De Geest, May 15 1999

Keywords

• nonn
• base
• easy

Examples

			a(16) = (1)(2)(3)(4)(5)(6)(7)(8)(9)(A)(B)(C)(D)(E)(F)(10) = 123456789ABCDEF10_16 = 20988295479420645136.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A014899.

Concatenation of first n numbers in other bases: 2: A047778, 3: A048435, 4: A048436, 5: A048437, 6: A048438, 7: A048439, 8: A048440, 9: A048441, 10: A007908, 11: A048442, 12: A048443, 13: A048444, 14: A048445, 15: A048446, 16: this sequence.

Programs

Magma

[n eq 1 select 1 else Self(n-1)*16^(1+Ilog(16, n))+n: n in [1..20]]; // Vincenzo Librandi, Dec 30 2012

Mathematica

If[STARTPOINT==1, n={}, n=Flatten[IntegerDigits[Range[STARTPOINT-1], 16]]]; Table[AppendTo[n, IntegerDigits[w, 16]]; n=Flatten[n]; FromDigits[n, 16], {w, STARTPOINT, ENDPOINT}] (* Dylan Hamilton, Aug 11 2010 *)
f[n_]:= FromDigits[Flatten@IntegerDigits[Range@n, 16], 16]; Array[f, 20] (* Vincenzo Librandi, Dec 30 2012 *)

Python

from functools import reduce
def A048447(n): return reduce(lambda i,j:(i<<(bool((m:=j.bit_length())&3)<<2)+(m&-4))+j,range(n+1)) # Chai Wah Wu, Feb 26 2023