A099649 -id:A099649 - cp's OEIS frontend

A099648 Largest term arising in complete-iteration-list (both transient and cycle) when f(x) = A003132(x) is iterated, i.e., if digit-squares of iterate added repeatedly until steady state (= either cycle or fixed point) is reached.

1, 145, 145, 145, 145, 145, 130, 145, 145, 10, 145, 145, 13, 145, 145, 145, 145, 145, 100, 145, 145, 145, 23, 145, 145, 145, 145, 100, 145, 145, 31, 32, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 44, 145, 145, 145, 145, 130, 145, 145, 145, 145, 145

Offset: 1

Labos Elemer, Nov 12 2004

			n=2: list = {2,4,16,37,58,89,145,42,20,4,16,37,58,...}; a(2) = max(list) = 145;
For n < 145, max > initial value except few cases. See A099649.

Cf. A003132, A031176, A099646, A099649.

ed[x_] :=IntegerDigits[x]; func[x_] :=Apply[Plus, ed[x]^2]; itef[x_, ho_] :=NestList[id2, x, 100]; Table[Max[Union[itef[w, 100]]], {w, 1, 256}]

A099652 Largest number arising if f[x]=1+A003132(x) function is iterated until steady state reached. Compare with A099648.

Original entry on oeis.org

107, 107, 107, 107, 107, 107, 107, 107, 118, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 118, 107, 107, 107, 107, 107, 118, 107, 107, 107, 107, 107, 107, 35, 53, 107, 107, 107, 107, 107, 107, 107, 107, 107, 53, 107, 107, 146, 107, 107, 107, 53

Offset: 1

Labos Elemer, Nov 12 2004

			n=32: list={32,14,18,66,73,59,107,51,27,54,42,21,6,37,59,107,51,...},
max[list]=a[32]=107>initial-value;
Also:lengths of transient=5,of cycle=0 (see in A099646).

Cf. A003132, A099648, A099646, A099649.

ed[x_] :=IntegerDigits[x];func[x_] :=Apply[Plus, ed[x]^2]+1; Table[Max[NestList[func, w, 200]], {w, 1, 150}]

cp's OEIS Frontend

A099648 Largest term arising in complete-iteration-list (both transient and cycle) when f(x) = A003132(x) is iterated, i.e., if digit-squares of iterate added repeatedly until steady state (= either cycle or fixed point) is reached.

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