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.

A236243 Position (or inverse of) n in A235598.

Original entry on oeis.org

0, 1, 2, 7, 10, 6, 4, 8, 35, 3, 67, 30, 5, 13, 89, 15, 143, 12, 22, 118, 385, 9, 11, 112, 19, 21, 23, 14, 355, 33, 26, 247, 69, 18, 70, 188, 17, 32, 61, 58, 888, 27, 20, 403, 871, 29, 250, 31, 65, 77, 1254, 55, 28, 57, 108, 59, 823, 34, 36, 633, 85, 116, 25, 80, 1710, 64, 238, 151, 1202, 54, 1677, 152, 53
Offset: 3

Views

Author

Robert G. Wilson v, Jan 22 2014

Keywords

Comments

The terms of this sequence are conjectured to be a permutation of the natural numbers.

Links

Crossrefs

Cf. A235598, A236244.

Programs

  • Mathematica
    (* run the Mmca in A235598 *); Flatten[ Table[ Position[ lst, n, 1, 1], {n, 3, 75}] - 1]

A236244 Records in A235598.

Original entry on oeis.org

3, 4, 5, 12, 15, 24, 25, 30, 80, 420, 1860, 146340, 292680, 3031080, 6355440, 202025100, 404050200, 674215920, 1309133280, 1759047480, 3141424023360, 6282848046720, 19013977277880, 2604166475512980, 295127694592600800, 1528966300926585360
Offset: 1

Views

Author

Robert G. Wilson v, Jan 22 2014

Keywords

Comments

These occur at positions: 0, 1, 2, 3, 5, 9, 11, 14, 16, 24, 37, 40, 123, 639, 926, 1040, 2263, 4266, 9242, 13783, 19157, 128911, 133369, 165603, 279520, 367234, …, .

Crossrefs

Cf. A235598, A236243.

Programs

  • Mathematica
    (* run the Mmca in A235598 *); k = 1; lsu = {}; mx = 0; While[k < 435000, If[lst[[k]] > mx, mx = lst[[k]]; Print[mx]; AppendTo[lsu, mx]]; k++]; lsu

A235599 Analog of A235598 if we start with 6.

Original entry on oeis.org

6, 8, 10, 24, 7, 25, 15, 9, 12, 5, 3, 4
Offset: 0

Views

Author

N. J. A. Sloane, Jan 17 2014, based on Jack Brennen's comments in A235598

Keywords

Comments

See discussion in A235598.

A239431 Consider the sequence A235598. Recalling that A235598(n) forms part of a Pythagorean triple, a(n) states its relationship to both a(n-1) and a(n+1). 1 denotes the lesser leg, 2 denotes the greater leg and 3 denotes the hypotenuse. The tens place returns its relationship to the side to its left, a(n-1), and the units place its relationship to the side to its right, a(n+1). a(0)=1.

Original entry on oeis.org

1, 22, 31, 22, 11, 32, 12, 11, 31, 22, 11, 33, 23, 21, 23, 11, 22, 13, 22, 11, 32, 12, 12, 31, 22, 13, 11, 22, 32, 12, 11, 33, 23, 21, 22, 11, 31, 22, 11, 31, 22, 11, 22, 31, 22, 13, 12, 13, 11, 21, 23, 12, 12, 13, 22, 11, 32, 12, 12, 31, 22, 11, 33, 13, 12, 11, 33, 11, 22, 12, 31, 22, 12, 12, 11, 31, 22, 11, 22, 12
Offset: 0

Views

Author

Robert G. Wilson v, Mar 20 2014

Keywords

Comments

Using the data that is available from Lars Blomberg, and the nine possible arrangements, (a), of the three sides, here are those counts for the first x terms not including a(0):
\x. 10 100 1000 10000 100000 1000000 3000000 aprx percentage.
a\
11:. 3. 21. 164. 1502. 13734. 134087. 401166 ~13.3%
12:. 1. 18. 215. 2120. 21457. 208304. 621859 ~20.7%
13:. 0.. 6.. 94.. 921.. 8884.. 86286. 256802. ~8.5%
21:. 0.. 3.. 51.. 550.. 5120.. 51732. 156588. ~5.2%
22:. 3. 22. 207. 2025. 21013. 214855. 646185 ~21.6%
23:. 0.. 5.. 55.. 657.. 6347.. 64480. 194775. ~6.5%
31:. 2. 12.. 95.. 881.. 8697.. 83631. 249413. ~8.3%
32:. 1.. 7.. 51.. 390.. 4219.. 42112. 126410. ~4.2%
33:. 0.. 6.. 68.. 954. 10529. 114513. 346802 ~11.7%

Examples

			a(2)=31 because 5 is the hypotenuse in the 3-4-5 Pythagorean triple, a(n-1) is 4 and 5 is the lesser side in the 5-12-13 Pythagorean triple, a(n+1) is 12.

Links

Crossrefs

Cf. A235598, A236243, A236244.

Programs

  • Mathematica
    lst={ (* the terms from A235598 *) }; g[j_, k_] := Block[{hyp = Sqrt[ j^2 + k^2], lg = Abs@ Sqrt[ j^2 - k^2]}, If[ IntegerQ@ hyp, If[ Min[j, k] == k, 1, 2], If[ Max[j, k] == k, 3, If[lg > k, 1, 2]]]]; f[n_] := Block[{s = Take[lst, {n - 1, n + 1}]}, 10g[ s[[1]], s[[2]] ] + g[ s[[3]], s[[2]] ]]; f[1] = 1; Array[f, 80]

A239381 a(0) = 3, the least length of a Primitive Pythagorean Triangle (PPT). a(n) is the least hypotenuse of a PPT which has a(n-1) as one of its legs.

Original entry on oeis.org

3, 5, 13, 85, 157, 12325, 90733, 2449525, 28455997, 295742792965, 171480834409967437, 656310093705697045, 1616599508725767821225590944157, 4461691012090851100342993272805, 115366949386695884000892071602798585632943213, 12002377162350258332845595301471273220420939451301220405
Offset: 0

Views

Author

Robert G. Wilson v, Mar 17 2014

Keywords

Comments

a(0)=3 because A042965(3)=3 with comments.
If we relax the Primitive restriction, i.e., GCD(x,y,z) can exceed 1, then we have A018928.

Examples

			a(0)=3 by definition,
a(1)=5 because it is the hypotenuse of a 3-4-5 PPT,
a(2)=13 because it is the hypotenuse of a 5-12-13 PPT,
a(3)=85 because it is the hypotenuse of a 13-84-85 PPT,
a(4)=157 because it is the hypotenuse of a 85-132-157 PPT, 85 is also the leg of a 85-3612-3613 PPT but its hypotenuse is larger, etc.

Links

Crossrefs

Cf. A008846, A235598.

Programs

  • Mathematica
    f[s_List] := Block[{x = s[[-1]]}, Append[s, Transpose[ Solve[x^2 + y^2 == z^2 && GCD[x, y, z] == 1 && y > 0 && z > 0, {y, z}, Integers]][[-1, 1, 2]]]]; lst = Nest[f, {3}, 15]

A239356 Begin with a(0) = 3. Let a(n) for n > 0 be the smallest positive integer not yet in the sequence which forms part of a Primitive Pythagorean Triple (PPT) when paired with a(n-1).

Original entry on oeis.org

3, 4, 5, 12, 13, 84, 85, 36, 77, 2964, 2573, 3925, 1116, 637, 1285, 893, 924, 43, 925, 372, 997, 497004, 497005, 138204, 82597, 161005, 39973, 155964, 386827, 417085, 258037, 327684, 139763, 356245, 225924, 82643, 240565, 37164, 13573, 39565, 2388, 39637, 26412, 11515, 28813
Offset: 0

Views

Author

Robert G. Wilson v, Mar 16 2014

Keywords

Comments

I.e., the GCD of a(n) and a(n-1) is 1. That is why a(4)= 13 as opposed to A235598(4), which is 9.
Is the sequence infinite? Probably. But will it eventually contain all the terms of A042965 which are greater than 2? Probably not.

Links

Crossrefs

Cf. A235598.

Programs

  • Mathematica
    f[s_List] := Block[{n = s[[-1]]}, sol = Solve[ x^2 + y^2 == z^2 && GCD[x, y, z] == 1 && x > 0 && y > 0 && z > 0 && (x == n || z == n), {x, y, z}, Integers]; Append[s, Min[ Complement[ Union[ Extract[ sol, Position[ sol, _Integer]]], s]]]]; lst = Nest[f, {3}, 25]
Showing 1-6 of 6 results.

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

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