A048436 Take the first n numbers written in base 4, concatenate them, then convert from base 4 to base 10.

1, 6, 27, 436, 6981, 111702, 1787239, 28595832, 457533321, 7320533146, 117128530347, 1874056485564, 29984903769037, 479758460304606, 7676135364873711, 491272663351917520, 31441450454522721297, 2012252829089454163026, 128784181061725066433683

Offset: 1

Author

Patrick De Geest, May 15 1999

Keywords

• nonn
• base
• easy

Comments

There is no prime among the first 5000 terms (emails from Kurt Foster, Oct 21 2015 and Oct 24 2015). When is the first prime? - N. J. A. Sloane, Oct 25 2015

There is no prime among the first 45000 terms. - Giovanni Resta, Jun 07 2018

Examples

			a(7): (1)(2)(3)(10)(11)(12)(13) = 12310111213_4 = 1787239.
		

Links

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

Crossrefs

Cf. A014825.

Concatenation of first n numbers in other bases: 2: A047778, 3: A048435, 4: this sequence, 5: A048437, 6: A048438, 7: A048439, 8: A048440, 9: A048441, 10: A007908, 11: A048442, 12: A048443, 13: A048444, 14: A048445, 15: A048446, 16: A048447. - Dylan Hamilton, Aug 11 2010

Programs

Magma

[n eq 1 select 1 else Self(n-1) * 4^(1+Ilog(4,n)) + n: n in [1..20]]; // Jason Kimberley, Nov 27 2012

Mathematica

a[n_]:= FromDigits[Flatten@IntegerDigits[Range@n, 4], 4]; Array[a, 20] (* Vincenzo Librandi, Dec 30 2012 *)

Python

from functools import reduce
def A048436(n): return reduce(lambda i,j:(i<<(bool((m:=j.bit_length())&1)<<1)+(m&-2))+j,range(n+1)) # Chai Wah Wu, Feb 26 2023

Formula

a(n) = a(n-1) * 4^(1 + floor(log4(n))) + n. [Moved from A117640 by Jason Kimberley, Nov 27 2012]