A093512 Transform of the prime sequence by the Rule73 cellular automaton.

1, 3, 4, 10, 16, 22, 26, 27, 28, 34, 35, 36, 40, 46, 50, 51, 52, 56, 57, 58, 64, 65, 66, 70, 76, 77, 78, 82, 86, 87, 88, 92, 93, 94, 95, 96, 100, 106, 112, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 130, 134, 135, 136, 142, 143, 144, 145, 146, 147, 148

Offset

1,2

Comments

As described in A051006, a monotonic sequence can be mapped into a fractional real. Then the binary digits of that real can be treated (transformed) by an elementary cellular automaton. Taken resulted sequence of binary digits as a fractional real, it can be mapped back into a sequence, as in A092855.

Links

Table of n, a(n) for n=1..61.

Ferenc Adorjan, Binary mapping of monotonic sequences - the Aronson and the CA functions

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Prog

(PARI) {ca_tr(ca, v)= /* Calculates the Cellular Automaton transform of the vector v by the rule ca */
local(cav=vector(8), a, r=[], i, j, k, l, po, p=vector(3));
a=binary(min(255, ca)); k=matsize(a)[2]; forstep(i=k, 1, - 1, cav[k-i+1]=a[i]);
j=0; l=matsize(v)[2]; k=v[l]; po=1;
for(i=1, k+2, j*=2; po=isin(i, v, l, po); j=(j+max(0, sign(po)))% 8; if(cav[j+1], r=concat(r, i)));
return(r) /* See the function "isin" at A092875 */}

Crossrefs

Cf. A092855, A051006, A093510, A093511, A093513, A093514, A093515, A093516, A093517.

Sequence in context: A007007 A037952 A281903 * A081160 A051437 A224073

Adjacent sequences: A093509 A093510 A093511 * A093513 A093514 A093515

Keyword

easy,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Status

approved