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 1-3 of 3 results.

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 *)

A219961 First differences of A219960.

Original entry on oeis.org

314, 11, 335, 110, 162, 25, 94, 47, 119, 21, 98, 377, 46, 97, 1, 151, 133, 97, 23, 194, 23, 53, 255, 5, 2, 24, 27, 21, 228, 238, 18, 47, 40, 64, 22, 48, 12, 56, 107, 22, 12, 86, 68, 89, 26, 200, 39, 30, 2, 95, 14, 21, 189, 21, 59, 19, 27, 63, 7, 44, 98, 40
Offset: 1

Views

Author

Carl R. White, Dec 02 2012

Keywords

Comments

Conjecture: 1 appears infinitely often in this sequence (indicating an infinite number of pairs of consecutive integers in the parent sequence), despite very few appearances compared with A219552, which is derived from a very similar process.

Links

Crossrefs

Cf. A219960, A219552, A219962

Programs

  • Mathematica
    f[n_] := Ceiling[Sqrt[n]]*(Ceiling[Sqrt[n]]^2 - n); t = Select[Range[10000], NestWhileList[f, #, UnsameQ, All][[-1]] > 0 &]; Differences[t] (* T. D. Noe, Dec 04 2012 *)

A219553 Records in A219552.

Original entry on oeis.org

6, 11, 12, 18, 56, 66, 105, 110, 130, 132, 139, 140, 185, 195, 197, 202, 261, 266, 313
Offset: 1

Views

Author

Carl R. White, Nov 22 2012

Keywords

Comments

313 found at x = 79142421 under the iteration of A219303. No more entries up to x = 101890000. - Carl R. White, Nov 30 2012

Crossrefs

Cf. A219303, A219552, A219962.

Extensions

a(17)-a(19) from Carl R. White, Nov 30 2012
Showing 1-3 of 3 results.

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

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