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 1-8 of 8 results.

A061839 a(n+1) is the smallest square ending with a(n), initial term is 5.

Original entry on oeis.org

5, 25, 225, 1225, 81225, 16281225, 7077116281225, 1642681227077116281225, 228822983661635570881642681227077116281225, 976324672198183536165095004791768497036228822983661635570881642681227077116281225
Offset: 1

Views

Author

Amarnath Murthy, May 29 2001

Keywords

Links

Crossrefs

Cf. A050634, A065689, A065780, A065781, A050636, A050638.

Extensions

Corrected and extended by Frank Ellermann, Jun 04 2001
More terms from Ulrich Schimke (ulrschimke(AT)aol.com), Dec 18 2001
Edited by N. J. A. Sloane, Apr 29 2007
First term prepended by Derek Orr, Dec 27 2013

A050630 a(n+1) is next smallest nontrivial square containing a(n) as a substring, initial term is 4.

Original entry on oeis.org

4, 49, 1849, 18496, 103184964, 7383508103184964, 544680602158273835081031849649
Offset: 1

Views

Author

Patrick De Geest, Jul 15 1999

Keywords

Crossrefs

Starting with a(2)=49, the sequence is identical A050632.
Cf. A050631, A048559, A050636.

Formula

a(n) = A050631(n)^2.

Extensions

a(7) from Max Alekseyev, Feb 15 2012

A065297 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) properly contained in the digits of a(n+1)^2, with a(0)=1.

Original entry on oeis.org

1, 4, 13, 36, 113, 487, 1036, 3214, 10456, 36786, 100963, 319656, 1001964, 3165969, 10001786, 31626854, 100013919, 316256807, 1000029656, 3162322481, 10000115537
Offset: 0

Views

Author

Floor van Lamoen, Oct 29 2001

Keywords

Comments

Probably infinite and at least O(10^(n/2)). - David W. Wilson

Examples

			13^2 = 169 and 36 is the next smallest number whose square (in this case 1296) properly contains the digits 1,6,9.

Crossrefs

Cf. A050630, A050631, A048559, A050636, A065298, A014563, A066825.
Cf. A000290, A000196.

Programs

  • Haskell
    import Data.List ((\\), sort)
a065297 n = a065297_list !! n
a065297_list = 1 : f 1 (drop 2 a000290_list) where
   f x (q:qs) | null (xs \\ sq) && sort xs /= sort sq = y : f y qs
              | otherwise                             = f x qs
              where y = a000196 q; sq = show q; xs = show (x * x)
-- Reinhard Zumkeller, Nov 22 2012

Extensions

More terms from Marc Paulhus, Jan 29 2002
More terms from David W. Wilson and Marc Paulhus, Feb 05 2002
a(19)-a(20) from Sean A. Irvine, Aug 26 2023

A061361 a(1) = 4; a(n) = least number such that the concatenation a(n)a(n-1)...a(2)a(1) is a square.

Original entry on oeis.org

4, 6, 17, 604, 9612, 85848855, 109457393440691436, 16484027824615378535694780556419522, 2537811713051483817817710620248313487995814710180147690293469081793581
Offset: 1

Views

Author

Amarnath Murthy, Apr 28 2001

Keywords

Examples

			a(3)a(2)a(1) = 1764 = 42^2, a(4)a(3)a(2)a(1) = 6041764 = 2458^2, a(5)a(4)a(3)a(2)a(1) = 8584885596126041764 = 2929997542^2.

Crossrefs

Cf. A050636, A050637, A061359, A061363.

Extensions

Corrected by Larry Reeves (larryr(AT)acm.org), May 07 2001
More terms from Ulrich Schimke (ulrschimke(AT)aol.com), Nov 06 2001

A050637 a(1) = 2; a(n+1)^2 is next smallest square ending with a(n)^2.

Original entry on oeis.org

2, 8, 42, 2458, 310042, 2929997542, 1046218875000310042, 406005268741864709999999997070002458, 50376698115810287966925579573179705000000000000000001046218875000310042
Offset: 1

Views

Author

Patrick De Geest, Jul 15 1999

Keywords

Crossrefs

Cf. A050636, A048560, A050631, A061361.
See A065789 for an essentially identical sequence.

Extensions

More terms from Ulrich Schimke (ulrschimke(AT)aol.com), Nov 06 2001

A065298 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) properly contained in the digits of a(n+1)^2, with a(0)=2.

Original entry on oeis.org

2, 7, 43, 136, 367, 1157, 3658, 10183, 32193, 101407, 320537, 1001842, 3166463, 10001923, 31627114, 100017313, 316599084, 1000104687, 3162331407, 10000483663
Offset: 0

Views

Author

Floor van Lamoen, Oct 29 2001

Keywords

Comments

a(n) for n>0 remains the same when a(0)=3.

Examples

			43^2 = 1849 and 136 is the next smallest number whose square (in this case 18496) properly contains the digits 1,4,8,9.

Crossrefs

Cf. A050630, A050631, A048559, A050636, A065297.

Extensions

More terms from Marc Paulhus, Feb 04 2002
a(18)-a(19) from Sean A. Irvine, Aug 26 2023

A065788 a(1) = 64; for n > 1 a(n) is the smallest square > a(n-1) with a(n-1) forming its final digits.

Original entry on oeis.org

64, 1764, 6041764, 96126041764, 8584885596126041764, 1094573934406914368584885596126041764, 164840278246153785356947805564195221094573934406914368584885596126041764
Offset: 1

Views

Author

Klaus Brockhaus, Nov 19 2001

Keywords

Comments

a(n) = A050636(n+1) for n >= 1.

Crossrefs

A050634, A050636, A065689, A065789, A065790.

Programs

  • Mathematica
    nxt[n_]:=Module[{k=1},While[!IntegerQ[Sqrt[k*10^IntegerLength[n]+n]],k++];k*10^IntegerLength[n]+n]; NestList[nxt,64,6] (* Harvey P. Dale, Dec 14 2019 *)

A065807 Squares with a smaller square as final digits.

Original entry on oeis.org

49, 64, 81, 100, 121, 144, 169, 225, 289, 324, 361, 400, 441, 484, 529, 625, 729, 784, 841, 900, 961, 1024, 1089, 1225, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364
Offset: 1

Views

Author

Klaus Brockhaus, Nov 22 2001

Keywords

Links

Crossrefs

A065808 gives the corresponding square roots.
Cf. A038678.
Cf. A065689, A050634, A050636, A050638, A065776, A061839, A065782, A065785, A065788, A065791.

Programs

  • Mathematica
    ds[n_] := NestWhileList[FromDigits[Rest[IntegerDigits[#]]] &, n, # > 9 &]; Select[Range[4, 58]^2, Or @@ IntegerQ /@ Sqrt[Rest[ds[#]]] &] (* Jayanta Basu, Jul 10 2013 *)
  • PARI
    a065807(m) = local(a, b, d, j, k, n); for(k=1, m, a=length(Str(n))-1; b=1; j=1; n=k^2; while(b, d=divrem(n, 10^j); if(d[1]>0&&issquare(d[2]), b=0; print1(n, ", "), if(j
  • PARI
    isokend(n) = my(p=10); for(k=1, #Str(n)-1, if (issquare(n % p), return (1)); p*=10);
isok(n) = issquare(n) && isokend(n); \\ Michel Marcus, Mar 17 2020

Extensions

Changed offset from 0 to 1 by Vincenzo Librandi, Sep 24 2013
Showing 1-8 of 8 results.

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

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