A387312 a(n) is the action of "Rule 30" elementary cellular automaton on the binary representation of n if the cells may only expand into the significant bits.

0, 3, 7, 6, 14, 13, 13, 12, 28, 31, 27, 26, 26, 25, 25, 24, 56, 59, 63, 62, 54, 53, 53, 52, 52, 55, 51, 50, 50, 49, 49, 48, 112, 115, 119, 118, 126, 125, 125, 124, 108, 111, 107, 106, 106, 105, 105, 104, 104, 107, 111, 110, 102, 101, 101, 100, 100, 103, 99, 98, 98, 97, 97, 96, 224, 227, 231, 230, 238, 237, 237, 236, 252

Offset: 0

Author

Mia Boudreau, Aug 25 2025

Keywords

• nonn
• new

Comments

A269160 allows cells to expand in both directions; its example gives 111 -> 11001 (as opposed to this 111 -> 1100). This sequence does not allow the cells to expand into the least significant bits.

A269160 is a subsequence.

When calculating the LSB edge, the out-of-bounds cell is taken to be 0.

Examples

			For a(7): 111 -> 1100, so a(7) = 12.
For a(10): 1010 -> 11011, so a(10) = A269160(5) = 27.
		

Links

• Mia Boudreau, Table of n, a(n) for n = 0..9999
• Eric Weisstein's World of Mathematics, Rule 30
• The Wolfram Atlas of Simple Programs, Rule 30

Crossrefs

Cf. A269160.

Programs

C

unsigned long long a(unsigned long long n){
 unsigned char rule = 30;
 unsigned long long x = 0;
 int l = sizeof(unsigned long long) * 8;
 for(int i = 0; i < l; i++)
  x|=((rule>>(((n>>(i+1)&(i>i&1)<<1)|(n>>(i-1)&(i>0))))&1)<
				

Formula

a(2*n) = A269160(n).