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 1-4 of 4 results.

A122986 Squares mod 1000.

Original entry on oeis.org

0, 1, 4, 9, 16, 24, 25, 36, 41, 44, 49, 56, 64, 76, 81, 84, 89, 96, 100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, 196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, 281, 284, 289, 296, 304, 316, 321, 324, 329, 336, 344
Offset: 1

Views

Author

Sergio Pimentel, Sep 22 2006

Keywords

Comments

Possible last three digits of n^2 (leading zeros omitted).
Range of A174452; A010461 is a subset; and also all squares less than 1000 belong to this sequence; the sequence is finite with A000993(3)=159 terms: a(159)=996 is the last term.

Examples

			The last three digits of n^2 can be 000, 001, 236, 241, 996, etc. but not 002, 003, 237, 238, etc.

Links

Crossrefs

Cf. A036688, A010382, A010411, A010462, A010421, A174452.
Cf. A006716, A053975, A027676, A027678, A122987, A122988.
Row 1000 of A096008.

Programs

  • Magma
    [n: n in [0..999] | IsSquare(R! n) where R:= ResidueClassRing(1000)]; // Vincenzo Librandi, Dec 29 2019
  • Maple
    s:={}: for n from 0 to 999 do s:=s union {n^2 mod 1000}: od: op(s); # Nathaniel Johnston, Jun 22 2011
  • Mathematica
    Union[PowerMod[Range[1000], 2, 1000]] (* Vincenzo Librandi, Dec 29 2019 *)

Extensions

More terms and additional comments from Reinhard Zumkeller, Mar 21 2010
Edited by N. J. A. Sloane, Apr 10 2010

A060557 Row sums of triangle A060556.

Original entry on oeis.org

1, 3, 10, 33, 108, 352, 1145, 3721, 12087, 39254, 127469, 413908, 1343980, 4363921, 14169633, 46008619, 149389218, 485064009, 1574993356, 5113971944, 16604963593, 53915979657, 175064088671
Offset: 0

Views

Author

Wolfdieter Lang, Apr 06 2001

Keywords

Comments

Equals the INVERT transform of A045623: (1, 2, 5, 12, 28, ...). - Gary W. Adamson, Oct 26 2010

Links

Crossrefs

a(n)=A028495(2n+1).
Cf. A053975.
Cf. A052975 (row sums of triangle A060102).
Cf. A045623. - Gary W. Adamson, Oct 26 2010

Programs

  • Mathematica
    a[0] = 1; a[1] = 3; a[2] = 10; a[n_] := a[n] = 5*a[n-1] - 6*a[n-2] + a[n-3]; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jul 05 2013, after Floor van Lamoen *)
LinearRecurrence[{5,-6,1},{1,3,10},30] (* Harvey P. Dale, Nov 29 2013 *)
  • PARI
    { f="b060557.txt"; a0=1; a1=3; a2=10; write(f, "0 1"); write(f, "1 3"); write(f, "2 10"); for (n=3, 500, write(f, n, " ", a=5*a2 - 6*a1 + a0); a0=a1; a1=a2; a2=a; ) } \\ Harry J. Smith, Jul 07 2009

Formula

a(n) = Sum_{m=0..n} A060556(n, m).
G.f.: (1-x)^2/(1 - 5*x + 6*x^2 - x^3).
a(n) = 5a(n-1) - 6a(n-2) + a(n-3). - Floor van Lamoen, Nov 02 2005

A053974 Numbers k such that k^2 contains only digits {6,8,9}.

Original entry on oeis.org

3, 83, 264, 836, 3114, 8167, 98336, 818333, 828667, 994836, 9309617, 984833336, 82885443167, 948097937383, 984879122886, 2588184048685235767383, 99483516217346127185182923658937
Offset: 1

Views

Author

Patrick De Geest, Mar 15 2000

Keywords

Links

Crossrefs

Cf. A053975.

Extensions

More terms from Gareth McCaughan, Jun 11 2004
a(16) from Mishima's website, added by Max Alekseyev, Nov 30 2017
a(17) from Zhao Hui Du, Apr 07 2024

A119234 Triangular numbers composed of digits {6,8,9}.

Original entry on oeis.org

6, 66, 666, 68898988866, 88698868996686886, 696999969866686966889999889666
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Comments

a(7) > 10^37. - Max Alekseyev, Apr 30 2010
a(7) > 10^40. - Tyler Busby, Mar 29 2023

Links

Crossrefs

Cf. A000217, A053975, A119235. See A119033 for a table of cross-references.

Formula

a(n) = A000217(A119235(n)). - Michel Marcus, Mar 27 2023
Showing 1-4 of 4 results.

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

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