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A074890
a(n) is the action of recursively applying 'Rule 30' elementary cellular automata on the binary representation of n if the cells may only expand into the significant bit, a(0) = 1.
5
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, 3731477134, 6741237465, 14952214679
OFFSET
0,2
COMMENTS
Previous name: Decimal form of binary integers produced by a modified version of Wolfram's Rule 30 one-dimensional cellular automaton.
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). - R. J. Mathar, Apr 29 2009
The out-of-bounds cell on the least significant bit's edge is taken to be 0. - Mia Boudreau, Sep 10 2025
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media Inc., (2002), p. 27.
LINKS
Eric Weisstein's World of Mathematics, Rule 30
The Wolfram Atlas of Simple Programs, Rule 30
FORMULA
a(n+1) = A387312(a(n)). - Mia Boudreau, Sep 10 2025
EXAMPLE
Initial terms:
1 (1)
11 (3)
110 (6)
1101 (13)
11001 (25)
110111 (55)
PROG
(Java)
BigInteger a(int n){
BigInteger k = BigInteger.ONE;
for(int t = 0; t < n; t++){
int RULE = 30;
BigInteger x = BigInteger.ZERO;
for(int i = 0; i < n+1; i++)
if((RULE>>((gb(k, i+1)<<2)|(gb(k, i)<<1)|gb(k, i-1))&1)>0) x=x.setBit(i);
k = x; }
return k; }
int gb(BigInteger b, int i){return b.shiftRight(i).testBit(0)?1:0; } // Mia Boudreau, Sep 10 2025
CROSSREFS
Cf. A110240, A387312, A269160 for Rule 30.
Sequence in context: A005116 A121349 A215984 * A244704 A032198 A079941
KEYWORD
base,nonn
AUTHOR
Jason E Sackett (jason(AT)heavyion.com), Sep 13 2002
EXTENSIONS
Definition modified by N. J. A. Sloane, Jul 28 2014
Entry revised by Mia Boudreau, Sep 11 2025
STATUS
approved