A093516 Transform of the prime sequence by the Rule137 cellular automaton.

1, 3, 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, 154

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, A093512, A093513, A093514, A093515, A093517.

Sequence in context: A092827 A087904 A242203 * A246302 A358792 A278041

Adjacent sequences: A093513 A093514 A093515 * A093517 A093518 A093519

Keyword

easy,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Status

approved