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.

A095347 n sets a new record for number of iterations of A034690 (sum of digits of the divisors of n) needed to reach 15 (see A086793).

Original entry on oeis.org

2, 5, 9, 10, 16, 18, 34, 36, 66, 162, 924, 71820, 127005777360
Offset: 1

Views

Author

Jason Earls, Jun 03 2004

Keywords

Comments

323203999999676796 takes 22 iterations to reach 15, but it probably is not the next term.
One could prefix a(0)=1 and change the definition to "... reach a fixed point, 1 or 15." - M. F. Hasler, Nov 08 2015

Links

Crossrefs

Cf. A034690, A086793, A094501.

Programs

Extensions

Offset corrected and a(13) from Donovan Johnson, Oct 28 2010

A119396 Numbers n such that A086793(n)=20.

Original entry on oeis.org

924, 1104, 1134, 1540, 1650, 1760, 1820, 1908, 1992, 2016, 2288, 2556, 2632, 2744, 2860, 2940, 2970, 3000, 3192, 3204, 3220, 3248, 3400, 3630, 3738, 3784, 3840, 3852, 3880, 3968, 3990, 4134, 4260, 4410, 4464, 4674, 4736, 4860, 4875, 4930, 4992, 5016
Offset: 1

Views

Author

Zak Seidov, May 17 2006

Keywords

Comments

Some trajectories are: 924,168,102,36,46,18,30,27,22,9,13,5,6,12,19,11,3,4,7,8,15 1104,168,102,... 1540,162,66,36,... 1650,162,66,36,... 2016,297,66,36,... 2940,297,66,36,... 3192,312,102,36,... All trajectories eventually join one of previous trajectories.

Examples

			924 is a term because it reaches 15 in 20 steps with this trajectory 924,168,102,36,46,18,30,27,22,9,13,5,6,12,19,11,3,4,7,8,15.

Links

Crossrefs

Cf. A034690, A086793, A094501, A095347, A114527, A118358, A119397, A119398, A260059.

Programs

  • Maple
    f:= proc(n) option remember; local t;
  if kernelopts(level) > 460 then return FAIL fi;
  t:= add(convert(convert(d,base,10),`+`),d=numtheory:-divisors(n));
  1+procname(t)
end proc:
f(15):= 0:
f(1):= FAIL:
Res:= NULL: count:= 0:
for n from 1 while count < 100 do
  if f(n) = 20 then
    count:= count+1;
    Res:= Res, n;
   fi
od:
Res; # Robert Israel, Apr 03 2018

Extensions

Edited by Robert Israel, Apr 03 2018

A260059 Infinite square array whose n-th row lists the numbers k for which A086793(k)=n, where A086793 = number of iteration of A034690 (sum of digits of divisors) to reach a fixed point, read by antidiagonals.

Original entry on oeis.org

8, 14, 7, 20, 21, 4, 26, 39, 35, 3, 59, 43, 44, 54, 2, 62, 52, 48, 56, 11, 19, 122, 57, 49, 128, 101, 37, 12, 123, 61, 50, 171, 136, 73, 64, 6, 143, 67, 65, 182, 138, 109, 108, 29, 5, 149, 84, 99, 188, 160, 127, 301, 33, 23, 13, 167, 93, 104, 216, 184, 163, 553, 47, 24, 31, 9, 206, 112, 105, 248, 190, 181, 589, 83, 28, 38, 25, 10, 239
Offset: 1

Views

Author

M. F. Hasler, Nov 08 2015

Keywords

Comments

The fixed points of A034690 are 1 and 15, these are the only numbers not appearing in this table. All other positive integers appear exactly once.
Is there a simple explanation why row 7 seems to grow significantly faster than the neighboring rows?
From row 21 on, the terms become very large: cf. A094501 which is the first column with 15 prefixed.

Examples

			The rows read
[ 8, 14,  20,  26,  59,  62, 122, 123, 143, 149, 167, 206, 239, 257, 293, 302,...],
[ 7, 21,  39,  43,  52,  57,  61,  67,  84,  93, 112, 124, 139, 151, 157, 189,...],
[ 4, 35,  44,  48,  49,  50,  65,  99, 104, 105, 116, 121, 125, 132, 140, 141,...],
[ 3, 54,  56, 128, 171, 182, 188, 216, 248, 252, 261, 264, 268, 270, 333, 387,...],
[ 2, 11, 101, 136, 138, 160, 184, 190, 208, 232, 238, 255, 282, 290, 318, 328,...],
[19, 37,  73, 109, 127, 163, 181, 271, 307, 396, 433, 523, 541, 613, 631, ...],
[12, 64, 108, 301, 553, 589, 949,1089,1197,1273,1687,1876,1957,2116, ...],
[ 6, 29,  33,  47,  83, 137, 173, 191, 227, 263, 281, 303, 317, ...],
[ 5, 23,  24,  28,  41,  42,  45,  92, 113, 131, 158, 164, ...],
[13, 31,  38,  60,  69,  74,  76,  77,  80,  86, 88, ...],
[ 9, 25,  72,  81, 117, 126, 156, 172, 258, 300, ...],
[10, 17,  22,  53,  71,  96, 107, 133, 202, ...], etc.
The first column is A094501.

Crossrefs

Cf. A034690, A086793, A094501.

Programs

  • PARI
    (f(k,N=20,a=[],n=0)=while(#aA086793(n++)==k&&a=concat(a,n));a); T=vector(20,n,f(n,21-n)); for(n=1,20,for(k=1,n,print1(T[k][n-k+1]",")))

A260060 Least number such that exactly n iterations of A034690 are required to reach one of the fixed points, 1 or 15.

Original entry on oeis.org

1, 8, 7, 4, 3, 2, 19, 12, 6, 5, 13, 9, 10, 16, 30, 18, 34, 36, 66, 162, 924, 71820
Offset: 0

Views

Author

M. F. Hasler, Nov 08 2015

Keywords

Comments

Apart from the initial term a(1), the same as A094501.

Examples

			The orbits are:
  {1},
  {8, 15},
  {7, 8, 15},
  {4, 7, 8, 15},
  {3, 4, 7, 8, 15},
  {2, 3, 4, 7, 8, 15},
  {19, 11, 3, 4, 7, 8, 15},
  {12, 19, 11, 3, 4, 7, 8, 15},
  {6, 12, 19, 11, 3, 4, 7, 8, 15},
  {5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {10, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {16, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {34, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {66, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {162, 66, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {924, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {71820, 1104, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15}

Links

Crossrefs

Cf. A034690, A086793, A094501, A095347.

Programs

  • PARI
    a(n)=for(k=1,9e9, A086793(k)==n&&return(k))
Showing 1-4 of 4 results.

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