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Search: id:A085308
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| A085308 |
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Iterate function described in A085308[=reverse concatenation of prime factors]; a(n) is either 1# the fixed point[=prime] if it exists at all: 2# a(2k)=1 labels that no convergence with most even initial values, in contrary mostly rapid divergence is the case; 3# a(n)=0 if n=1 or if the iteration results in nontrivial attractor with cycle length larger than one. |
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4
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| 0, 2, 3, 2, 5, 2, 7, 2, 3, 1, 11, 2, 13, 2, 53, 2, 17, 2, 19, 1, 73, 2, 23, 2, 5, 1, 3, 2, 29, 1, 31, 2, 113, 2, 53, 2, 37, 2, 197, 1, 41, 1, 43, 2, 53, 1, 47, 2, 7, 1, 173, 1, 53, 2, 41113, 2, 193, 1, 59, 1, 61, 1, 73, 2, 53, 1, 67, 1, 233, 1, 2, 73, 1, 53, 1, 197, 1, 79, 1, 3, 1, 83, 1, 53, 1
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Algorithm: 1# factorize n; 2# arrange prime-factors by decreasing size; 3# concatenate prime factors and interpret the result as decimal number.
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EXAMPLE
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n=even: remains even: m=100=2.2.5.5 ->{2,5} ->{5,2} ->52=a(100);
n=2^i.3^j: a(n)=2 since iteration list is {n,32,2}; these
are the known convergent even cases of initial value.
n=143: a(143)=44864859110711 because the iteration list is
{143,1311,23193,8593,66113,388917,547793,2273241,55311373,
989474313,8914183373,84859143973,528059391607,44864859110711};
a(n)= 0 for n=213,323,639,713 ending in
{713,3123,3473,15123} terminal orbit of length=4.
All possible cases occur: fixed p., divergence,terminal cycle.
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] rec[x_] := Fold[nd, 0, Flatten[IntegerDigits[Reverse[ba[x]]], 1]] Table[rec[w], {w, 1, 128}]
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CROSSREFS
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Cf. A084317-A084319, A085308, A085309.
Sequence in context: A076199 A136096 A072591 this_sequence A086286 A135679 A092028
Adjacent sequences: A085305 A085306 A085307 this_sequence A085309 A085310 A085311
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KEYWORD
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base,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 27 2003
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