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Search: id:A084318
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| A084318 |
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Iterate function described in A084317 if started at initial value n until reaching a fixed point. |
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+0
6
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| 0, 2, 3, 2, 5, 23, 7, 2, 3, 5, 11, 23, 13, 3, 1129, 2, 17, 23, 19, 5, 37, 211, 23, 23, 5, 3251, 3, 3, 29, 547, 31, 2, 311, 31397, 1129, 23, 37, 373, 313, 5, 41, 379, 43, 211, 1129, 223, 47, 23, 7, 5, 317, 3251, 53, 23, 773, 3, 1129, 229, 59, 547, 61, 31237, 37, 2, 1129, 2311
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: fixed point always exists.
Some initial values capriciously provide very large prime fixed-points. This behavior is illustrated in A084319 for initial value n=91.
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EXAMPLE
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a(0)=0 since no prime factors to concatenate;
a[p^j]=p for p prime(powers);
n=95=519: fixed-point list is {95,519,3173,19167,36389},
so a(95)=36389, a prime.
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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] conc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[FixedPoint[conc, w], {w, 1, 90}] Table[conc[w], {w, 1, 128}]
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CROSSREFS
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Cf. A084317, A084319.
Sequence in context: A086507 A133568 A120716 this_sequence A084317 A037279 A106736
Adjacent sequences: A084315 A084316 A084317 this_sequence A084319 A084320 A084321
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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 16 2003
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