A219960 -id:A219960 - cp's OEIS frontend

A219961 First differences of A219960.

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

Carl R. White, Dec 02 2012

nonn

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.

Carl R. White, Table of n, a(n) for n = 1..10000

Cf. A219960, A219552, A219962

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 *)

A219962 Records in A219961.

Original entry on oeis.org

314, 335, 337, 535, 539, 615, 666

Offset: 1

Carl R. White, Dec 02 2012

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

Cf. A219960, A219961, A219553.

More terms from Carl R. White, Dec 05 2012

A219963 Numbers which do not reach zero under either of the iterations: x -> floor(sqrt(x)) * (x - floor(sqrt(x))^2) or y -> ceiling(sqrt(y)) * (ceiling(sqrt(y))^2 - y).

Original entry on oeis.org

2897, 3159, 3183, 4004, 6335, 7025, 8163, 8237, 8621, 9234, 12204, 12963, 13381, 14340, 15217, 16191, 16438, 17474, 17763, 17972, 18065, 18990, 19677, 19848, 20345, 20803, 21426, 21539, 22022, 25834, 26872, 27175, 28052, 28929, 28996, 29295, 30511, 30991

Offset: 1

Carl R. White, Dec 02 2012

nonn

Intersection of A219303 and A219960.
Like the parent sequences, this sequence has pairs of consecutive integers; The first of these pairs is 89971 and 89972.
It is possible, assuming the infinite-pairs conjectures are true for both parent sequences, that there may also be an infinite number of pairs here, but even then that is not guaranteed.

Carl R. White, Table of n, a(n) for n = 1..10000

Cf. A219303, A219960.

cp's OEIS Frontend

A219961 First differences of A219960.

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A219962 Records in A219961.

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A219963 Numbers which do not reach zero under either of the iterations: x -> floor(sqrt(x)) * (x - floor(sqrt(x))^2) or y -> ceiling(sqrt(y)) * (ceiling(sqrt(y))^2 - y).

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