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A030623 Powers of 2 grouped in pairs of 2 digits (version 2). 3

%I #14 Mar 28 2020 19:21:16

%S 12,48,16,32,64,12,82,56,51,21,2,42,4,84,9,68,19,21,63,84,32,76,86,55,

%T 36,13,10,72,26,21,44,52,42,88,10,48,57,62,9,71,52,41,94,30,48,38,86,

%U 8,16,77,72,16,33,55,44,32,67,10,88,64,13,42,17,72,82,68,43,54,56,53,68

%N Powers of 2 grouped in pairs of 2 digits (version 2).

%C When a 0 occurs as the most significant digit of the pair, it is simply ignored, e.g., "02" becomes just 2. The following pairs are unaffected. - _Alonso del Arte_, Mar 28 2020

%e The first few powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192. The digits are 1, 2, 4, 8, 1, 6, 3, 2, 6, 4, 1, 2, 8, 2, 5, 6, 5, 1, 2, 1,0, 2, 4, 2, 0, 4, 8, 4, 0, 9, 6. Grouping them in pairs, we obtain 12, 48, 16, 32, 64, 12, 82, 56, 51, 21, 02, 42, 04, 84, 09, 68, etc.

%p sq:=[]: for n from 0 to 100 do s:=convert(2^n,base,10): l:=nops(s): sq:=[op(sq),seq(s[l-i],i=0..l-1)] od: seq(sq[2*i-1]*10+sq[2*i],i=1..100); # C. Ronaldo

%t FromDigits/@Partition[Flatten[IntegerDigits[2^Range[0, 63]]], 2] (* _Alonso del Arte_, Mar 28 2020 *)

%o (Scala) (List.fill(63)(2: BigInt)).scanLeft(1: BigInt)(_ * _).map(_.toString.toCharArray).flatten.sliding(2, 2).map(_.toArray).toList.map(new String(_)).map(Integer.parseInt(_)) // _Alonso del Arte_, Mar 28 2020

%Y Cf. A030622, A030624, A000079, A000455.

%K nonn,base,easy

%O 1,1

%A Alexei Kozlowski (bros(AT)spf.minsk.by)

%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 03 2005

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)