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 1-6 of 6 results.

A114611 Eventual period of the RATS sequence, where 0 indicates a divergent sequence.

Original entry on oeis.org

0, 0, 8, 0, 0, 8, 0, 0, 2, 0, 0, 8, 0, 0, 8, 0, 0, 2, 0, 0, 8, 0, 0, 8, 0, 0, 2, 0, 18, 8, 0, 0, 8, 0, 0, 2, 0, 18, 8, 0, 0, 8, 0, 0, 2, 0, 18, 8, 18, 0, 8, 0, 0, 2, 0, 18, 8, 18, 0, 8, 0, 0, 2, 0, 18, 8, 18, 0, 2, 0, 0, 2, 0, 18, 8, 18, 0, 2, 0, 0, 2, 0, 18, 8, 18, 0, 2, 0, 0, 2, 0, 18, 8, 18, 0, 2
Offset: 1

Views

Author

Eric W. Weisstein, Dec 16 2005

Keywords

Comments

a(A001651(n)) = 0; a(A114612(n)) = 2; a(A114613(n)) = 3; a(A114614(n)) = 8; a(A114615(n)) = 14; a(A114616(n)) = 18. - Reinhard Zumkeller, Mar 14 2012
Row 10 of A288537. - Andrey Zabolotskiy, Jun 14 2017

Links

Crossrefs

Cf. A036839, A161593, A288536, A288537.

A066710 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 3.

Original entry on oeis.org

3, 6, 12, 33, 66, 123, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333
Offset: 1

Views

Author

N. J. A. Sloane, Jan 19 2002

Keywords

Comments

a(1) = A114614(1) = 3; A114611(3) = 8. [Reinhard Zumkeller, Mar 14 2012]

Examples

			668 -> 668 + 866 = 1534 -> 1345.

Links

Crossrefs

Cf. A004000, A036839, A066711, A209878, A209879, A209880.

Programs

  • Haskell
    a066710_list = iterate a036839 3  -- Reinhard Zumkeller, Mar 14 2012
  • Mathematica
    f[k_] := Module[{m = FromDigits[Reverse[IntegerDigits[k]]]}, FromDigits[ Sort[ IntegerDigits[k + m]]]]; NestList[f, 3, 50] (* Harvey P. Dale, Jan 18 2011 *)

Formula

Let a(n) = k, form m by Reversing the digits of k, Add m to k Then Sort the digits of the sum into increasing order to get a(n+1).
Periodic with period 8.
a(n+1) = A036839(a(n)). [Reinhard Zumkeller, Mar 14 2012]
From Chai Wah Wu, Feb 07 2020: (Start)
a(n) = a(n-8) for n > 14.
G.f.: x*(-99*x^13 - 45*x^12 - 44523*x^11 - 12321*x^10 - 3483*x^9 - 1674*x^8 - 888*x^7 - 444*x^6 - 123*x^5 - 66*x^4 - 33*x^3 - 12*x^2 - 6*x - 3)/(x^8 - 1). (End)

A114612 Starting numbers for which the RATS sequence has eventual period 2.

Original entry on oeis.org

9, 18, 27, 36, 45, 54, 63, 69, 72, 78, 81, 87, 90, 96, 99, 108, 114, 117, 120, 126, 135, 144, 153, 156, 162, 171, 180, 189, 198, 207, 213, 216, 225, 234, 243, 252, 255, 261, 270, 279, 288, 297, 306, 312, 315, 324, 333, 342, 351, 354, 360, 369, 378, 387, 396
Offset: 1

Views

Author

Eric W. Weisstein, Dec 16 2005

Keywords

Comments

A114611(a(n)) = 2. - Reinhard Zumkeller, Mar 14 2012

Links

Crossrefs

Cf. A114611, A114612, A114613, A114614, A114615, A114616.
Cf. A066711, A036839.

A114613 Starting numbers for which the RATS sequence has eventual period 3.

Original entry on oeis.org

20169, 20709, 21159, 22149, 23139, 24129, 25119, 26109, 27099, 28089, 29079, 30159, 30168, 30708, 30789, 31149, 31158, 31779, 32139, 32148, 32769, 33129, 33138, 33759, 34119, 34128, 34749, 35109, 35118, 35739, 36108, 36729, 37098
Offset: 1

Views

Author

Eric W. Weisstein, Dec 16 2005

Keywords

Comments

A114611(a(n)) = 3. - Reinhard Zumkeller, Mar 14 2012

Links

Crossrefs

Cf. A114611, A114612, A114613, A114614, A114615, A114616.
Cf. A209878, A036839.

A114615 Starting numbers for which the RATS sequence has eventual period 14.

Original entry on oeis.org

6999, 7089, 7179, 7269, 7359, 7449, 7539, 7629, 7719, 7809, 7998, 8088, 8178, 8268, 8358, 8448, 8538, 8628, 8718, 8808, 8997, 9087, 9177, 9267, 9357, 9447, 9537, 9627, 9699, 9717, 9789, 9807, 9879, 9969, 9996, 10128, 10167, 10185, 10191
Offset: 1

Views

Author

Eric W. Weisstein, Dec 16 2005

Keywords

Comments

A114611(a(n)) = 14. - Reinhard Zumkeller, Mar 14 2012

Links

Crossrefs

Cf. A114611, A114612, A114613, A114614, A114615, A114616.
Cf. A209879, A036839.

A114616 Starting numbers for which the RATS sequence has eventual period 18.

Original entry on oeis.org

29, 38, 47, 49, 56, 58, 65, 67, 74, 76, 83, 85, 92, 94, 110, 112, 118, 134, 137, 140, 142, 154, 155, 181, 187, 196, 209, 211, 217, 229, 233, 236, 239, 241, 253, 254, 259, 280, 286, 295, 299, 308, 310, 316, 319, 328, 329, 332, 335, 338, 340, 352, 353, 358
Offset: 1

Views

Author

Eric W. Weisstein, Dec 16 2005

Keywords

Comments

A114611(a(n)) = 18. - Reinhard Zumkeller, Mar 14 2012

Links

Crossrefs

Cf. A114611, A114612, A114613, A114614, A114615, A114616.
Cf. A209880, A036839.
Showing 1-6 of 6 results.

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

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