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 1-7 of 7 results.

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.

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

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

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

See A065789 for an essentially identical sequence.

Extensions

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

A050639 a(1) = 3; a(n+1)^2 is next smallest square ending with a(n)^2.

Original entry on oeis.org

3, 7, 43, 1293, 154957, 20214998707, 118659019449999845043, 5566692951015284052000000000020214998707, 21637689578064053873124753714430240419600000000000000000000118659019449999845043
Offset: 1

Views

Author

Patrick De Geest, Jul 15 1999

Keywords

Crossrefs

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

Extensions

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

A050633 a(1)=3; for n>1, a(n)^2 is next smallest nontrivial square containing a(n-1)^2 as a substring.

Original entry on oeis.org

3, 7, 43, 136, 10158, 85927342, 738024797793593
Offset: 1

Views

Author

Patrick De Geest, Jul 15 1999

Keywords

Crossrefs

Starting with a(2)=7, the sequence is identical to A050631.

Formula

a(n) = sqrt(A050632(n)).

Extensions

a(7) from Max Alekseyev, Feb 15 2012

A050629 a(n+1)^2 is next smallest nontrivial square containing a(n)^2 as a substring, initial term is 1.

Original entry on oeis.org

1, 4, 13, 237, 6013, 3655347, 6491041181267
Offset: 1

Views

Author

Patrick De Geest, Jul 15 1999

Keywords

Crossrefs

Formula

a(n) = sqrt(A050628(n)).

Extensions

a(7) from Max Alekseyev, Feb 15 2012
Showing 1-7 of 7 results.