cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A099647 Function f[n]=1+Sum[digit^2 of n] is iterated as in A099646. Values x for which A099646[x]=1 are listed here. These terms are analogous to happy-numbers [=A007770].

Original entry on oeis.org

35, 36, 46, 53, 57, 63, 64, 75, 135, 138, 153, 156, 165, 183, 237, 245, 246, 254, 264, 273, 279, 297, 305, 306, 315, 318, 327, 334, 343, 347, 350, 351, 360, 372, 374, 381, 388, 406, 425, 426, 433, 437, 452, 460, 462, 473, 503, 507, 513, 516, 524, 530, 531
Offset: 1

Views

Author

Labos Elemer, Nov 11 2004

Keywords

Comments

Iteration g[x] applied in A031176 is slightly modified to obtain actual function to iterate here: f[x]=1+g[x].Initial values resulting in fixed points are collected.

Examples

			n=35 is here because list={36,46,53,[35],35,...} with transient t=3, c=1 cycle-length.

Crossrefs

Cf. A031176, A099645, A007770, A099646.

Programs

  • Mathematica
    ed[x_] :=IntegerDigits[x]; f[x_] :=Apply[Plus, ed[x]^2]+1; itef[x_, ho_] :=NestList[f, x, ho]; tmc=Table[Length[Union[itef[w, 100]]], {w, 1, 256}]; c1=Table[Min[Flatten[Position[itef[w, Length[Union[itef[w, 100]]]] -Last[itef[w, Length[Union[itef[w, 100]]]]], 0]]], {w, 1, 256}]; Flatten[Position[tmc-(c1-1), 1]]

A099649 Solutions to A099648(k) > k, i.e., numbers such that the largest term in the iteration of the A003132() function strictly exceeds the initial value.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79
Offset: 1

Views

Author

Labos Elemer, Nov 12 2004

Keywords

Comments

The last term I encountered was a(130) = 144. Is this sequence finite? Is a(130) = 144 the final term?

Examples

			For n=7, the list of values in the trajectory is {7,49,97,130,10,1,1,1,1,1,1,1,...}; max = 130 > 7 = n, so 7 is in the sequence.
For n=32, list = {32,13,10,1,1,...}; max = 32 = n, so 32 is not in the sequence.
The sequence includes all positive integers < 145 except {1,10,13,23,31,32,44,100,103,109,129,130,133,139}.

Crossrefs

Cf. A003132, A031176, A099646, A099649.

Programs

  • Mathematica
    ed[x_] :=IntegerDigits[x]; func[x_] :=Apply[Plus, ed[x]^2]; itef[x_, ho_] :=NestList[id2, x, 100]; ta={{0}};Do[s=Max[Union[itef[w, 100]]]; If[Greater[s, w], Print[w];ta=Append[ta, w]], {w, 1, 10000000}]; Delete[ta, 1]

Extensions

Edited by Jon E. Schoenfield, Nov 26 2017

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.

Original entry on oeis.org

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

Views

Author

Labos Elemer, Nov 12 2004

Keywords

Examples

			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.

Crossrefs

Cf. A003132, A031176, A099646, A099649.

Programs

  • Mathematica
    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

Views

Author

Labos Elemer, Nov 12 2004

Keywords

Examples

			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).

Crossrefs

Cf. A003132, A099648, A099646, A099649.

Programs

  • Mathematica
    ed[x_] :=IntegerDigits[x];func[x_] :=Apply[Plus, ed[x]^2]+1; Table[Max[NestList[func, w, 200]], {w, 1, 150}]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.