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.

A256410 Subtract 1 from the terms of A256407.

Original entry on oeis.org

2, 197, 269, 521, 569, 599, 821, 881, 1061, 1949, 2129, 2267, 2309, 2591, 2969, 3167, 5021, 5501, 6701, 7349, 9437, 10037, 10427, 10499, 14009, 14561, 15287, 16649, 17027, 17957, 18059, 18521, 19697, 19889, 20549, 20717, 20771, 22157, 22637, 23057, 23561, 24107, 25169
Offset: 1

Views

Author

N. J. A. Sloane, Apr 03 2015

Keywords

Comments

Conjectured to be always a prime. But which primes are these? It would be nice to know of some other property that distinguishes these primes. See also the "blog" in A166133.

Links

Crossrefs

Cf. A166133, A256403-A256409.

A166133 After initial 1,2,4, a(n+1) is the smallest divisor of a(n)^2-1 that has not yet appeared in the sequence.

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, 69, 28, 27, 26, 25, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 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, 201, 80, 79
Offset: 1

Views

Author

Franklin T. Adams-Watters, Oct 07 2009

Keywords

Comments

The initial 1,2,4 provides the smallest example with this rule that is not simply the integers in order, nor (apparently) ends with all divisors of a(n)^2-1 already present.
Apparently the sequence is infinite and includes every positive integer.
Apr 05 2015: John Mason has computed the first ten million terms. See link to zipped file. - N. J. A. Sloane, Apr 06 2015
The sequence contains many runs of incrementing and decrementing values. In the 1200 steps following the 4, there are 136 increments, 706 decrements, and 358 larger steps. What is the limiting distribution for these steps? [Click the "listen" button to appreciate these runs. - N. J. A. Sloane, Apr 03 2015]
After 3, 198, 270, 570, 522, 600, 822, and 882, we have a(n+1) = a(n)^2-1. Does this happen infinitely often? Cf. A256406, A256407.
A256543 gives numbers m such that a(m+1) = a(m)-1 or a(m+1) = a(m)+1. - Reinhard Zumkeller, Apr 01 2015
If this is a permutation, then A255833 is the inverse permutation. - M. F. Hasler, Apr 01 2015
a(A256703(n)+1) = a(A256703(n))^2 - 1. - Reinhard Zumkeller, Apr 08 2015
For n > 3: a(n) = A027750(a(n-1)^2-1, A256751(n)). - Reinhard Zumkeller, Apr 09 2015

Examples

			After a(24) = 22, the divisors of 22^2-1 = 483 are 1, 3, 7, 21, 23, 69, 161, and 483; 1, 3, 7, 21, and 23 have already occurred, so a(25) = 69.

Links

Crossrefs

Cf. A166134, A000027, A122280, A005563, A256406, A256407, A027750, A005563, A256557, A256559.
For records see A256403, A256404.
Smallest missing numbers: A256405, A256408, A256409.
Cf. A256541 (first differences), A256543.
Inverse (conjectured): A255833.
Cf. A256564 (smallest prime factors), A244080 (largest prime factors), A256578 (largest proper divisors), A256542 (number of divisors).
Upper envelope: the sequence of pairs (A256422(n),A256423(n)).
Cf. A256703.
Cf. A256751.

Programs

  • Haskell
    import Data.List (delete); import Data.List.Ordered (isect)
a166133 n = a166133_list !! (n-1)
a166133_list = 1 : 2 : 4 : f (3:[5..]) 4 where
   f zs x = y : f (delete y zs) y where
            y = head $ isect (a027750_row' (x ^ 2 - 1)) zs
-- Reinhard Zumkeller, Apr 01 2015
  • Mathematica
    s = {1, 2, 4}; e = 4; Do[d = Divisors[e^2 - 1]; i = 1;
While[MemberQ[s, d[[i]]], i++]; e = d[[i]]; AppendTo[s, e], {19997}]; s (* Hans Havermann, Apr 03 2015 *)
  • PARI
    al(n,m=4,u=6)={local(ds,db);
u=bitor(u,1<

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
Showing 1-3 of 3 results.

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

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