A102256 Begin with 1, multiply each digit by 2, separate the digits.
1, 2, 4, 8, 1, 6, 2, 1, 2, 4, 2, 4, 8, 4, 8, 1, 6, 8, 1, 6, 2, 1, 2, 1, 6, 2, 1, 2, 4, 2, 4, 2, 1, 2, 4, 2, 4, 8, 4, 8, 4, 2, 4, 8, 4, 8, 1, 6, 8, 1, 6, 8, 4, 8, 1, 6, 8, 1, 6, 2, 1, 2, 1, 6, 2, 1, 2, 1, 6, 8, 1, 6, 2, 1, 2, 1, 6, 2, 1, 2, 4, 2, 4, 2, 1, 2, 4, 2, 4, 2, 1, 2, 1, 6, 2, 1, 2, 4, 2, 4, 2, 1, 2, 4, 2
Offset: 1
Examples
Read a(4)=8 which produces, doing 8*2=16 ["1" & "6"], a(5)=1 & a(6)=6. Now read a(5)=1 which produces [a(6) is already written] a(7)=2 because 1*2=2. Now read a(6)=6 which produces [a(7) is already written] a(8)=1 & a(9)=2 because 6*2=12 ["1" & "2"].
Programs
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Mathematica
Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[ 2IntegerDigits[ x]]]], 1, 14]] (* Robert G. Wilson v, Feb 21 2005 *)
Extensions
More terms from Robert G. Wilson v, Feb 21 2005
Comments