A093511 Transform of the prime sequence by the Rule45 cellular automaton.

1, 3, 5, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 22, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 40, 42, 43, 44, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 61, 62, 64, 65, 66, 68, 70, 72, 73, 74, 76, 77, 78, 80, 82, 84, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 100, 102, 103, 104

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..70.

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, A093512, A093513, A093514, A093515, A093516, A093517.

Sequence in context: A080218 A080651 A047330 * A039041 A079253 A076054

Adjacent sequences: A093508 A093509 A093510 * A093512 A093513 A093514

Keyword

easy,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Status

approved