A093517 Transform of the prime sequence by the Rule225 cellular automaton.

1, 4, 5, 7, 10, 13, 16, 19, 22, 26, 27, 28, 31, 34, 35, 36, 40, 43, 46, 50, 51, 52, 56, 57, 58, 61, 64, 65, 66, 70, 73, 76, 77, 78, 82, 86, 87, 88, 92, 93, 94, 95, 96, 100, 103, 106, 109, 112, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 130, 134, 135, 136, 139

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..64.

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, A093516.

Sequence in context: A013947 A202342 A234141 * A248858 A145018 A018910

Adjacent sequences: A093514 A093515 A093516 * A093518 A093519 A093520

Keyword

easy,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Status

approved