A048436 - OEIS

%I #47 Feb 26 2023 13:16:33

%S 1,6,27,436,6981,111702,1787239,28595832,457533321,7320533146,

%T 117128530347,1874056485564,29984903769037,479758460304606,

%U 7676135364873711,491272663351917520,31441450454522721297,2012252829089454163026

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

%C 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

%C There is no prime among the first 45000 terms. - _Giovanni Resta_, Jun 07 2018

%H Vincenzo Librandi, <a href="/A048436/b048436.txt">Table of n, a(n) for n = 1..200</a>

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

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

%t a[n_]:= FromDigits[Flatten@IntegerDigits[Range@n, 4], 4]; Array[a, 20] (* _Vincenzo Librandi_, Dec 30 2012 *)

%o (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

%o (Python)

%o from functools import reduce

%o 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

%Y Cf. A014825.

%Y 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

%K nonn,base,easy

%O 1,2

%A _Patrick De Geest_, May 15 1999