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.

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A219962 Records in A219961.

Original entry on oeis.org

314, 335, 337, 535, 539, 615, 666
Offset: 1

Views

Author

Carl R. White, Dec 02 2012

Keywords

Comments

The first member of this sequence is currently (Dec 02 2012) one greater than the largest member yet found of cousin sequence A219553. Therein the value of 313 required significant time to determine. This is almost surely a coincidence, though it would be very interesting if it were not.
666 found at x = 72231492 under the iteration of A219960. No more entries up to x = 100400000

Crossrefs

Cf. A219960, A219961, A219553.

Extensions

More terms from Carl R. White, Dec 05 2012

A219960 Numbers which do not reach zero under the repeated iteration x -> ceiling(sqrt(x)) * (ceiling(sqrt(x))^2 - x).

Original entry on oeis.org

366, 680, 691, 1026, 1136, 1298, 1323, 1417, 1464, 1583, 1604, 1702, 2079, 2125, 2222, 2223, 2374, 2507, 2604, 2627, 2821, 2844, 2897, 3152, 3157, 3159, 3183, 3210, 3231, 3459, 3697, 3715, 3762, 3802, 3866, 3888, 3936, 3948, 4004, 4111, 4133, 4145, 4231, 4299
Offset: 1

Views

Author

Carl R. White, Dec 02 2012

Keywords

Comments

Ceiling equivalent of A219303, with somewhat different behavior despite a near-identical iterative process.
Conjecture #1: All numbers under the iteration reach 0 or, like the elements of this sequence, reach a finite loop, and none expand indefinitely to infinity.
Conjecture #2: There are an infinite number of such finite loops, though there is often significant distance between them.
Conjecture #3: There are an infinite number of pairs of consecutive integers in this sequence despite being less abundant than in A219303.

Examples

			1702 is in this list as 38 iterations return to 1702. Many other numbers reach this loop. 5832 is also in this list and is the smallest member of a different loop.
1703 is _not_ in this list because the iteration runs: 1703 -> 2562 -> 1989 -> 1620 -> 2501 -> 5100 -> 6048 -> 2808 -> 53 -> 88 -> 120 -> 11 -> 20 -> 25 -> 0.

Links

Crossrefs

Cf. A219303, A219961, A219962, A219963

Programs

  • Mathematica
    f[n_] := Ceiling[Sqrt[n]]*(Ceiling[Sqrt[n]]^2 - n); Select[Range[5000], NestWhileList[f, #, UnsameQ, All][[-1]] > 0 &] (* T. D. Noe, Dec 04 2012 *)
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