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 bit.

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

0,2

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 bit.

A269160 is a subsequence.

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

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.

Formula

a(n) = Sum_{i=0..floor(log_2(n)+1)} 2^i * b(30, 4*b(n,i+1) + 2*b(n,i) + b(n,i-1)), where b(n,i) = floor(n/(2^i)) mod 2.

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

a(n) = (n OR 2*n) XOR floor(n/2). - Mia Boudreau, May 15 2026

Example

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

Mathematica

A387312[n_] := BitXor[BitOr[n, 2*n], Quotient[n, 2]];
Array[A387312, 100, 0] (* Paolo Xausa, May 20 2026 *)

Prog

(C)
unsigned long long a(unsigned long long n){return (n>>1)^(n|n<<1); }

Crossrefs

Cf. A269160.

Sequence in context: A070882 A109635 A095360 * A175142 A318466 A324819

Adjacent sequences: A387309 A387310 A387311 * A387313 A387314 A387315

Keyword

nonn,base,easy

Author

Mia Boudreau, Aug 25 2025

Status

approved