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

12, 48, 16, 32, 64, 12, 82, 56, 51, 21, 2, 42, 4, 84, 9, 68, 19, 21, 63, 84, 32, 76, 86, 55, 36, 13, 10, 72, 26, 21, 44, 52, 42, 88, 10, 48, 57, 62, 9, 71, 52, 41, 94, 30, 48, 38, 86, 8, 16, 77, 72, 16, 33, 55, 44, 32, 67, 10, 88, 64, 13, 42, 17, 72, 82, 68, 43, 54, 56, 53, 68

Offset: 1

Author

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

Keywords

• nonn
• base
• easy

Comments

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

Examples

			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.
		

Crossrefs

Cf. A030622, A030624, A000079, A000455.

Programs

Maple

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

Mathematica

FromDigits/@Partition[Flatten[IntegerDigits[2^Range[0, 63]]], 2] (* Alonso del Arte, Mar 28 2020 *)

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

Extensions

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