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 1-10 of 34 results. Next

A135385 Fixed points of the map m -> powertrain(m) (see A133500 for definition).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2592, 24547284284866560000000000
Offset: 1

Views

Author

J. H. Conway and N. J. A. Sloane, Dec 11 2007, Dec 19 2007

Keywords

Comments

Probably there are no other terms. There are no other terms below 10^100.

Examples

			Under the powertrain map of A133500, 2^5*3^4 = 2592 -> 2^5*9^2 = 2592.
2^46*3^6*5^10*7^2 = 24547284284866560000000000 -> 2^4*5^4*7^2*8^4*2^8*4^8*6^6*5^6*0^0*0^0*0^0*0^0*0^0 = 24547284284866560000000000.

Links

  • N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.
  • N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

A135384 Numbers which converge to 2592 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

642, 2164, 2534, 2592, 3425, 6421, 9225, 10642, 11642, 12642, 13642, 14642, 15642, 16642, 17642, 18642, 19642, 20642, 21636, 21641, 22348, 22633, 22928, 23344, 23629, 23924, 24336, 24342, 24922, 25329, 25333, 25341, 25919, 25921, 30642, 31634, 32259
Offset: 1

Views

Author

J. H. Conway and N. J. A. Sloane, Dec 10 2007

Keywords

Comments

Many of these numbers reach 2592 in one step. Examples of numbers which take more than one step are 45756, 52648, 63724, 64528, 72634, 75456.

Links

Crossrefs

Cf. A133500, A135385.

Programs

A309385 Numbers which converge to 24547284284866560000000000 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

6672898, 6689728, 7266898, 7289668, 8966728, 8972668, 23667289, 23668972, 23726689, 23728966, 23896672, 23897266, 26667288, 26668872, 26726688, 26728866, 26886672, 26887266, 29367289, 29368972, 29667287, 29668772, 29723689, 29726687, 29728766, 29728936, 29728993, 29729389, 29876672, 29877266, 29893672, 29897236, 29897293, 29899372, 29937289, 29938972
Offset: 1

Views

Author

Martin Renner, Jul 27 2019

Keywords

Examples

			6672898 -> 6^6*7^2*8^9*8 = 2454728428486656 -> 2^4*5^4*7^2*8^4*2^8*4^8*6^6*5^6 = 24547284284866560000000000.

Links

Crossrefs

Cf. A133500, A135384, A135385, A326733, A326734, A326735, A326736, A326737, A326738, A326739, A326740, A326741, A326742.

A326735 Numbers which converge to 2 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

2, 21, 28, 36, 44, 62, 93, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 202, 211, 227, 229, 247, 256, 258, 263, 264, 272, 281, 286, 293, 302, 317, 324, 336, 342, 344, 349, 353, 358, 361, 376, 382, 402, 417, 419, 427, 433, 434, 441, 446, 456, 497, 502, 552
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			28 -> 2^8 = 256 -> 2^5*6 = 192 -> 1^9*2 = 2.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326736, A326737, A326738, A326739, A326740, A326741, A326742.

Programs

  • Python
    # change target for A326733-A326742, A135384, A309385
def powertrain(n):
  p, s = 1, str(n)
  if len(s)%2 == 1: s += '1'
  for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)
  return p
def aupto(limit, target=0):
  alst = []
  for n in range(1, limit+1):
    m, ptm = n, powertrain(n)
    while m != ptm: m, ptm = ptm, powertrain(ptm)
    if m == target: alst.append(n)
  return alst
print(aupto(552, target=2)) # Michael S. Branicky, Feb 21 2021

A326733 Numbers which converge to 0 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

0, 26, 35, 37, 38, 39, 43, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 64, 65, 66, 67, 68, 69, 72, 73, 74, 76, 77, 78, 79, 82, 84, 85, 86, 87, 88, 89, 94, 95, 96, 97, 98, 99, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 236, 237, 238, 239
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			26 -> 2^6 = 64 -> 6^4 = 1296 -> 1^2*9^6 = 531441 -> 5^3*1^4*4^1 = 500 -> 5^0*0 = 0.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326734, A326735, A326736, A326737, A326738, A326739, A326740, A326741, A326742.

A326734 Numbers which converge to 1 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 29, 30, 40, 42, 45, 50, 60, 63, 70, 80, 83, 90, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 215, 216, 217, 218, 219, 223, 224, 225, 226, 232, 233, 235, 241, 245, 257, 268, 274, 278, 282, 284, 285
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			24 -> 2^4 = 16 -> 1^6 = 1.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326735, A326736, A326737, A326738, A326739, A326740, A326741, A326742.

A326736 Numbers which converge to 3 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

3, 31, 103, 113, 123, 133, 143, 153, 163, 173, 183, 193, 203, 303, 311, 403, 503, 603, 703, 803, 903, 1031, 1131, 1231, 1331, 1431, 1531, 1631, 1731, 1831, 1931, 2031, 3031, 3100, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 3120, 3130, 3140
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			31 -> 3^1 = 3.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326737, A326738, A326739, A326740, A326741, A326742.

A326737 Numbers which converge to 4 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

4, 22, 41, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 204, 212, 221, 249, 304, 404, 411, 429, 504, 604, 624, 704, 804, 904, 1022, 1041, 1122, 1141, 1222, 1241, 1322, 1341, 1422, 1441, 1522, 1541, 1622, 1641, 1722, 1741, 1822, 1841, 1922, 1941, 2022
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			249 -> 2^4*9 = 144 -> 1^4*4 = 4.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326736, A326738, A326739, A326740, A326741, A326742.

A326738 Numbers which converge to 5 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

5, 51, 53, 105, 115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 305, 335, 345, 405, 455, 505, 511, 525, 527, 531, 537, 605, 692, 705, 745, 805, 875, 905, 925, 1051, 1053, 1151, 1153, 1251, 1253, 1351, 1353, 1451, 1453, 1551, 1553, 1651, 1653, 1751, 1753
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			53 -> 5^3 = 125 -> 1^2*5 = 5.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326736, A326737, A326739, A326740, A326741, A326742.

A326739 Numbers which converge to 6 under repeated application of the powertrain map of A133500.

Original entry on oeis.org

6, 61, 106, 116, 126, 136, 146, 156, 166, 176, 186, 196, 206, 213, 306, 312, 406, 506, 606, 611, 706, 724, 746, 806, 906, 1061, 1161, 1261, 1361, 1461, 1561, 1661, 1761, 1861, 1961, 2061, 2131, 2272, 2596, 3061, 3121, 3765, 3863, 4061, 4172, 4572, 5061, 6061
Offset: 1

Views

Author

Martin Renner, Jul 22 2019

Keywords

Examples

			724 -> 7^2*4 = 196 -> 1^9*6 = 6.

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326736, A326737, A326738, A326740, A326741, A326742.
Showing 1-10 of 34 results. Next

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

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