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 1-10 of 25 results. Next

A256403 Records in A166133.

Original entry on oeis.org

1, 2, 4, 8, 12, 16, 21, 24, 69, 201, 213, 319, 469, 519, 1141, 2321, 39203, 72899, 324899, 359999, 675683, 777923, 1127843, 4536899, 6718463, 10036223, 30272003, 44916803, 54022499, 100761443, 108743183, 110249999, 212051843, 233722943, 289952783, 326163599
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2015

Keywords

Comments

See the "blog" file in A166133 for discussion.

Links

Crossrefs

Cf. A166133, A256404.

A244080 Largest prime factor of A166133(n).

Original entry on oeis.org

1, 2, 2, 3, 2, 7, 3, 5, 3, 11, 5, 3, 2, 5, 7, 13, 7, 5, 19, 3, 17, 3, 23, 11, 23, 7, 3, 13, 5, 13, 19, 37, 3, 7, 17, 11, 2, 31, 5, 29, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 5, 17, 13, 53, 3, 11, 7, 19, 29, 59, 5, 61, 31, 7, 2, 13, 11, 67, 17, 67, 5, 79, 13, 11
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 02 2015

Keywords

Comments

a(n) = A006530(A166133(n)).

Links

Crossrefs

Cf. A166133, A006530, A256564, A256578.

Programs

  • Haskell
    a244080 = a006530 . a166133

A256404 Positions of records in A166133.

Original entry on oeis.org

1, 2, 3, 5, 9, 13, 17, 22, 25, 70, 82, 158, 174, 184, 194, 261, 293, 331, 616, 745, 983, 1076, 1672, 2177, 2821, 3599, 6591, 7804, 10174, 11629, 13141, 13397, 15589, 17767, 18814, 19859, 21112, 21247, 23242, 24785, 34351, 36447, 40122, 45630
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2015

Keywords

Links

Crossrefs

Cf. A166133, A256403.

A256409 a(n) = index of A256408(n) in A166133.

Original entry on oeis.org

1, 2, 4, 8, 12, 16, 21, 24, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 81, 93, 102, 111, 114, 163, 171, 198, 199, 259, 281, 292, 302, 426, 433, 451, 533, 550, 585, 586, 617, 747
Offset: 1

Views

Author

N. J. A. Sloane, Apr 03 2015, following a suggestion from Ray Chandler

Keywords

Comments

Created in order to try to understand the growth-rate of A256405 (and A166133). See the "blog" file in A166133.
Where records occur in A256405. - Ray Chandler, Apr 06 2015

Links

  • N. J. A. Sloane and John Mason, Table of n, a(n) for n = 1..199 [Terms 1 through 86 were computed by N. J. A. Sloane; terms 87 through 199 by John Mason, Apr 05 2015]

Crossrefs

Cf. A166133, A256405, A256408.

A255833 Index i such that A166133(i)=n, or 0 if no such i exists.

Original entry on oeis.org

1, 2, 4, 3, 8, 7, 6, 5, 12, 11, 10, 9, 16, 15, 14, 13, 21, 20, 19, 18, 17, 24, 23, 22, 29, 28, 27, 26, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 25
Offset: 1

Views

Author

M. F. Hasler, Apr 01 2015

Keywords

Comments

If A166133 is a permutation, as conjectured, then this is the inverse permutation.

Links

Crossrefs

Cf. A166133, A256561, A256563.

Programs

  • Haskell
    import Data.List (elemIndex); import Data.Maybe (fromJust)
a255833 = (+ 1) . fromJust . (`elemIndex` a166133_list)
-- Reinhard Zumkeller, Apr 02 2015
  • PARI
    a(n)=for(i=1,#a166133,a166133[i]==n&&return(i)) \\ assumes a166133 defined as a vector, e.g., via {c=0; a166133=apply(t->eval(concat(Vec(t)[1+#Str(c++) .. -1])), readstr("/tmp/b166133.txt"))}

Extensions

Definition simplified by Franklin T. Adams-Watters, Apr 01 2015

A256405 a(n) = smallest missing number after seeing A166133(n).

Original entry on oeis.org

2, 3, 3, 5, 5, 5, 5, 9, 9, 9, 9, 13, 13, 13, 13, 17, 17, 17, 17, 17, 22, 22, 22, 25, 25, 25, 25, 25, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2015

Keywords

Comments

The distinct terms are listed in A256408. See also A256409.
See the "blog" file in A166133 for discussion.

Links

Crossrefs

Cf. A166133, A027750, A005563, A256408, A256409.

Programs

  • Haskell
    import Data.List (delete); import Data.List.Ordered (isect)
a256405 n = a256405_list !! (n-1)
a256405_list = 2 : 3 : f (3:[5..]) 4 where
   f zs@(z:_) x = z : f (delete y zs) y where
                  y = head $ isect (a027750_row' (x ^ 2 - 1)) zs
-- Reinhard Zumkeller, Apr 01 2015

A256407 Numbers n such that for some m, A166133(m)=n, A166133(m+1)=n^2-1, in increasing order.

Original entry on oeis.org

3, 198, 270, 522, 570, 600, 822, 882, 1062, 1950, 2130, 2268, 2310, 2592, 2970, 3168, 5022, 5502, 6702, 7350, 9438, 10038, 10428, 10500, 14010, 14562, 15288, 16650, 17028, 17958, 18060, 18522, 19698, 19890, 20550, 20718, 20772, 22158, 22638, 23058, 23562, 24108, 25170, 25602
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2015

Keywords

Comments

Subtracting 1 seems always to give a prime - see A256410.

Links

Crossrefs

Cf. A166133, A256410. This is A256406 sorted into increasing order.

A256408 List of successive smallest missing numbers in A166133.

Original entry on oeis.org

2, 3, 5, 9, 13, 17, 22, 25, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 81, 86, 89, 97, 100, 146, 153, 154, 169, 196, 198, 249, 253, 300, 337, 340, 409, 411, 412, 414, 449, 587, 589, 610, 625, 958, 1201, 1202
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2015

Keywords

Comments

A256405 with duplicates omitted.
See the "blog" file in A166133 for discussion.
Records in A256405. - Ray Chandler, Apr 06 2015

Links

Crossrefs

Cf. A166133, A256405, A256409.

A256406 Numbers n such that for some m, A166133(m)=n, A166133(m+1)=n^2-1, in order of increasing m.

Original entry on oeis.org

3, 198, 270, 570, 522, 600, 822, 882, 1062, 2130, 1950, 2592, 2268, 2310, 3168, 2970, 5502, 6702, 5022, 7350, 10038, 10428, 10500, 9438, 14562, 14010, 15288, 17028, 18060, 19698, 17958, 19890, 18522, 20772, 29670, 20550, 22158, 16650
Offset: 1

Views

Author

N. J. A. Sloane, Apr 01 2015, based on a comment of Franklin T. Adams-Watters in A166133

Keywords

Comments

In other words, the next term in A166133 after n is as large as it can be. Terms are listed in order of appearance in A166133.
With the exception of the initial 3, the terms appear to be a (permuted) subset of A014574; i.e. the divisors of a(n)^2-1 are 1, a(n)-1, a(n)+1, and a(n)^2-1. - Hans Havermann, Apr 03 2015
See the "blog" file in A166133 for discussion.

Links

  • Hans Havermann and John Mason, Table of n, a(n) for n = 1..6575 [Terms 1 through 480 were computed by Hans Havermann; terms 481 through 6575 by John Mason, Apr 05 2015]

Crossrefs

Cf. A014574, A166133, A256407 (sorted version).

Programs

  • Haskell
    a256406 n = a256406_list !! (n-1)
a256406_list = f a166133_list where
   f (u:vs'@(v:ws)) | u > v || v /= u ^ 2 - 1 = f vs'
                    | otherwise               = u : f ws
-- Reinhard Zumkeller, Apr 01 2015

A256422 Numbers n such that A166133(n) sets a new record and also satisfies A166133(n)=A166133(n-1)^2-1.

Original entry on oeis.org

5, 293, 331, 616, 745, 983, 1076, 1672, 2177, 2821, 3599, 6591, 7804, 10174, 11629, 13141, 13397, 15589, 17767, 18814, 19859, 21112, 21247, 23242, 24785, 34351, 36447, 40122, 45630, 48033, 51235, 51519, 61179, 63826, 73394, 78624, 80112, 88259, 89607, 102217, 115981, 119167
Offset: 1

Views

Author

N. J. A. Sloane, Apr 08 2015

Keywords

Comments

A subsequence of A256404.
The points (A256422(i), A256423(i)) form the upper envelope of A166133.

Examples

			A166133(5) = 8 = A166133(4)^2-1 = 9-1.

Links

Crossrefs

Cf. A166133, A256423, A256404, A256403, A256703.

Formula

Intersection of A256404 and A256703+1. - Ray Chandler, Apr 13 2015
Showing 1-10 of 25 results. Next

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

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