A074890 Decimal form of binary integers produced by a modified version of Wolfram's Rule 30 one-dimensional cellular automaton.

1, 3, 6, 13, 25, 55, 100, 222, 401, 891, 1602, 3559, 6428, 14258, 25647, 56936, 102860, 228154, 410339, 910998, 1645813, 3650437, 6565453, 14576121, 26332935, 58407052, 105047514, 233217299, 421327294, 934513441, 1680759539

Offset: 0

Author

Jason E Sackett (jason(AT)heavyion.com), Sep 13 2002

Keywords

• base
• nonn

Comments

According to the common nomenclature (see A110240), this is actually a Rule 86 for all but the least-significant bit, and a Rule 252 for the least-significant bit, because the (fractional) bits right from the binary dot are never set. As a side effect, the first 11 terms--not the 12th--can be reproduced by a(n)=floor(A110240(n)/2^n). [From R. J. Mathar, Apr 29 2009]

Examples

			a(4)=13 because a(3)=6=0110(binary) and applying Rule 30 to each digit [(b(n)==0 && b(n+1)==0) ? b(n-1) : 1-b(n-1)]
		

References

• S. Wolfram, A New Kind of Science, Wolfram Media Inc., (2002), p. 27.

Crossrefs

Cf. A110240 for Rule 30.

Programs

Java

/** Java class to generate sequence */
public class r30seqA { static String zero="0",one="1"; public static void main(String[] args) { int base10 = 1; System.out.println(base10); for(int i=0; i<30; i++) System.out.println(base10 = base10Convert(applyR30(Integer.toBinaryString(base10)))); }
static String applyR30(String base2) { int a0,a1,a2,newDigit; StringBuffer newBase2 = new StringBuffer(); for(int i=-1; i
				

Formula

If b(n) is current binary digit, perform for each digit to get next integer in sequence: b(n) = (b(n)==0 && b(n+1)==0) ? b(n-1) : 1-b(n-1);//Wolfram's Rule 30*

Extensions

Definition modified by N. J. A. Sloane, Jul 28 2014