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.

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A256751 Index of A166133(n) in the list of divisors of A166133(n-1)^2 - 1.

Original entry on oeis.org

2, 4, 3, 5, 2, 7, 2, 8, 3, 7, 4, 6, 4, 10, 8, 4, 12, 2, 11, 3, 10, 6, 11, 4, 8, 6, 12, 10, 4, 12, 4, 12, 8, 7, 4, 14, 2, 19, 5, 21, 3, 17, 7, 9, 7, 13, 4, 19, 7, 13, 5, 17, 5, 21, 9, 11, 5, 17, 3, 17, 7, 9, 13, 17, 5, 17, 6, 12, 5, 24, 4, 16, 12, 8, 6, 15, 2
Offset: 4

Views

Author

Reinhard Zumkeller, Apr 09 2015

Keywords

Comments

A166133(n) = A027750(A166133(n-1)^2-1,a(n)).

Examples

			n = 12: A166133(12) = 9, A166133(12-1) = 10, 10^2 - 1 = 99,
9 is the third term of divisors(99) = [1,3,9,11,33,99],
therefore a(12) = 3;
n = 13: A166133(13) = 16, A166133(13-1) = 9, 9^2 - 1 = 80,
16 is the seventh term of divisors(80) = [1,2,4,5,8,10,16,20,40,80],
therefore a(13) = 7.

Links

Crossrefs

Cf. A166133, A027750.

Programs

  • Haskell
    import Data.List (elemIndex); import Data.Maybe (fromJust)
a256751 n = (+ 1) $ fromJust $
            a166133 n `elemIndex` a027750_row' (a166133 (n - 1) ^ 2 - 1)

A167381 The numbers read down the left-center column of an arrangement of the natural numbers in square blocks.

Original entry on oeis.org

1, 3, 6, 10, 14, 18, 23, 29, 35, 41, 47, 53, 60, 68, 76, 84, 92, 100, 108, 116, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215, 226, 238, 250, 262, 274, 286, 298, 310, 322, 334, 346, 358, 371, 385, 399, 413, 427, 441, 455, 469, 483, 497, 511, 525, 539, 553
Offset: 1

Views

Author

Paul Curtz, Nov 02 2009

Keywords

Comments

The natural numbers are filled into square blocks of edge length 2, 4, 6, 8, ...
by taking A016742(n+1) = 4, 16, 36, ... at a time:
.......1..2......
.......3..4......
....5..6..7..8...
....9.10.11.12...
...13.14.15.16...
...17.18.19.20...
21.22.23.24.25.26
27.28.29.30.31.32
33.34.35.36.37.38
39.40.41.42.43.44
Reading down the column just left from the center yields a(n).
The length of the rows is given by A001670.
The number of elements in each square block, 4, 16, 36, etc., are the first differences of A166464:
A016742(n) = A166464(n)-A166464(n-1).
Reading the blocks from right to left, row by row, we obtain a permutation of the integers, which starts similar to A166133.

Links

Crossrefs

Cf. A113127, A167991 (first differences).

Programs

  • Mathematica
    r[1] = Range[4]; r[n_] := r[n] = Range[r[n-1][[-1]]+1, r[n-1][[-1]]+(2n)^2 ];
s[n_] := Partition[r[n], Sqrt[Length[r[n]]]][[All, n]];
A167381 = Table[s[n], {n, 1, 7}] // Flatten (* Jean-François Alcover, Mar 26 2017 *)
Module[{nn=7,c},c=TakeList[Range[(2/3)*nn(nn+1)(2*nn+1)],(2*Range[ nn])^2]; Table[Take[c[[n]],{n,-1,2*n}],{n,nn}]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 18 2018 *)

Extensions

Edited by R. J. Mathar, Aug 29 2010
More terms from Jean-François Alcover, Mar 26 2017

A256543 Numbers m such that A256541(m) = -1 or = +1.

Original entry on oeis.org

1, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 22, 23, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 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, 71, 72, 73, 74, 75, 76, 77, 78
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 02 2015

Keywords

Comments

abs(A166133(n+1) - A166133(n)) = abs(A256541(n)) = 1.

Links

Crossrefs

Cf. A256541, A166133.

Programs

  • Haskell
    a256543 n = a256543_list !! (n-1)
a256543_list = [x | x <- [1..], abs (a256541 x) == 1]

A166134 a(n+1) is the smallest divisor of a(n)^2+1 that does not yet appear in the sequence, with a(1) = 1.

Original entry on oeis.org

1, 2, 5, 13, 10, 101, 5101, 26, 677, 45833, 65, 2113, 446477, 130, 16901, 41, 29, 421, 17, 58, 673, 45293, 25, 313, 97, 941, 34057, 50, 61, 1861, 1229, 773, 59753, 89, 34, 1157, 82, 269, 194, 617, 38069, 55740337, 145, 10513, 11052317, 12215371106849
Offset: 1

Views

Author

Franklin T. Adams-Watters, Oct 07 2009

Keywords

Comments

All members of the sequence can be represented as the sum of two relatively prime numbers (A008784). It appears that the sequence is infinite and that all such numbers are present.

Examples

			After a(4)=13, the divisors of 13^2+1=170 are 1,2, 5, 10, 17, 34, 85, 170. 1, 2, and 5 have already occurred, so a(5) = 10.

Links

Crossrefs

Cf. A166133, A008784, A031439, A002522.

Programs

  • Mathematica
    Nest[Append[#, Min[Complement[Divisors[#[[-1]]^2 + 1], #]]] &, {1}, 45] (* Ivan Neretin, Sep 03 2015 *)
  • PARI
    invec(v,x,n)=for(i=1,n,if(v[i]==x,return(1)));0
bl(n)={local(v,d,ds);
v=vector(n,i,1);
for(i=2,n,
ds=divisors(v[i-1]^2+1);
for(k=2,#ds,d=ds[k];if(!invec(v,d,i-1),v[i]=d;break)));
v}

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.
Previous Showing 21-25 of 25 results.

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

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