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.

A067633 a(1) = 1; sequence of digits of a(n)^2 is a subsequence of the sequence of digits of a(n+1)^2.

Original entry on oeis.org

1, 4, 13, 37, 117, 367, 3667, 36667, 366667, 3666667, 36666667, 366666667, 3666666667, 36666666667, 366666666667, 3666666666667, 36666666666667, 366666666666667, 3666666666666667, 36666666666666667, 366666666666666667, 3666666666666666667, 36666666666666666667
Offset: 1

Views

Author

David W. Wilson, Feb 05 2002

Keywords

Comments

Probably infinite. Does the obvious pattern continue?
The pattern continues until at least n=100 and is unlikely to change because insertion of 2 digits into a(n)^2 is sufficient to maintain the pattern. - Sean A. Irvine, Dec 28 2023

Links

Crossrefs

Cf. A014563, A066825, A068175.

Formula

a(n) = sqrt(A068175(n)). - Sean A. Irvine, Dec 28 2023

Extensions

Revised with data from A091874 by Sean A. Irvine, Dec 28 2023

A068176 a(1) = 2; for n>1, a(n) is the smallest square > a(n-1) obtained by inserting digits into a(n-1).

Original entry on oeis.org

2, 25, 225, 1225, 13225, 133225, 10336225, 1033622500, 103362250000, 10336225000000, 1033622500000000, 103362250000000000, 10336225000000000000, 1033622500000000000000, 103362250000000000000000
Offset: 1

Views

Author

Amarnath Murthy, Feb 25 2002

Keywords

Examples

			a(2) = 25. hence a(3) = 225 the smallest square formed from 25.

Crossrefs

Cf. A068175, A091875 gives square roots.

Extensions

Corrected and extended by Ray Chandler, Oct 11 2003

A068177 a(1) = 3; for n>1, a(n) is the smallest square > a(n-1) obtained by inserting digits into a(n-1).

Original entry on oeis.org

3, 36, 361, 32761, 323761, 32137561, 3211375561, 321113755561, 32111137555561, 3211111375555561, 321111113755555561, 32111111137555555561, 3211111111375555555561, 321111111113755555555561
Offset: 1

Views

Author

Amarnath Murthy, Feb 25 2002

Keywords

Examples

			a(2)=36, hence a(3) = 361 the smallest square formed from 36.

Crossrefs

Cf. A068175, A068176, A091876 gives square roots.

Extensions

Corrected and extended by Ray Chandler, Oct 11 2003

A068178 a(1) = 4; for n>1, a(n) is the smallest square > a(n-1) obtained by inserting digits into a(n-1).

Original entry on oeis.org

4, 49, 1849, 18496, 1784896, 177848896, 17778488896, 1777784888896, 177777848888896, 17777778488888896, 1777777784888888896, 177777777848888888896, 17777777778488888888896
Offset: 1

Views

Author

Amarnath Murthy, Feb 25 2002

Keywords

Examples

			a(2)=49 hence a(3) = 1849 the smallest square formed from 49.

Crossrefs

Cf. A068175, A068176, A068177, A091877 gives square roots.

Extensions

Corrected and extended by Ray Chandler, Oct 11 2003

A068616 Starting from a(1)=7, each subsequent term is the minimal square obtained by inserting at least one digit into the previous term.

Original entry on oeis.org

7, 576, 5476, 54756, 1547536, 154753600, 15475360000, 1547536000000, 154753600000000, 15475360000000000, 1547536000000000000, 154753600000000000000, 15475360000000000000000
Offset: 1

Views

Author

Amarnath Murthy, Feb 25 2002

Keywords

Examples

			a(2)=576 hence a(3) = 5476 the smallest square formed from 576.

Links

Crossrefs

Cf. A068175, A068176, A068177, A068178.

Programs

  • Maple
    Digits := 30 : isContain := proc(n,k) local ndigs,kdigs,f,d ; ndigs := convert(n,base,10) ; kdigs := convert(k,base,10) ; f := 1 : for d from 1 to nops(ndigs) do if f > nops(kdigs) then RETURN(false) ; fi ; while op(f,kdigs) <> op(d,ndigs) do f := f+1 ; if f > nops(kdigs) then RETURN(false) ; fi ; od: f := f+1 ; od: RETURN(true) ; end: n := 7 ; s := 8 : while true do while not isContain(n,s^2) do s := s+1 : od ; print(s^2) ; n := s^2: s := ceil(sqrt(s^2+1)) : od: # R. J. Mathar, Jun 26 2007
  • Mathematica
    Join[{7,576,5476,54756},NestList[100#&,1547536,10]] (* Harvey P. Dale, Jul 22 2024 *)

Formula

For n>=5, a(n) = 1547536*100^(n-5).
From Chai Wah Wu, Aug 03 2020: (Start)
a(n) = 100*a(n-1) for n > 5.
G.f.: x*(3928064*x^4 + 492844*x^3 + 52124*x^2 + 124*x - 7)/(100*x - 1). (End)

Extensions

More terms from R. J. Mathar, Jun 26 2007
5 more terms from Sean A. Irvine, Sep 27 2009
Edited by Max Alekseyev, Oct 12 2009

A091874 Duplicate of A067633.

Original entry on oeis.org

1, 4, 13, 37, 117, 367, 3667, 36667, 366667, 3666667, 36666667, 366666667, 3666666667, 36666666667, 366666666667, 3666666666667, 36666666666667, 366666666666667, 3666666666666667, 36666666666666667, 366666666666666667
Offset: 1

Views

Author

Ray Chandler, Feb 07 2004

Keywords

Crossrefs

Cf. A067633, A068175.

A068617 Starting from a(1)=8, each subsequent term is the minimal square obtained by inserting at least one digit in the previous term.

Original entry on oeis.org

8, 81, 841, 38416, 3841600, 384160000, 38416000000, 3841600000000, 384160000000000, 38416000000000000, 3841600000000000000, 384160000000000000000, 38416000000000000000000
Offset: 1

Views

Author

Amarnath Murthy, Feb 25 2002

Keywords

Comments

The growing square sequence for 1 and 6, 2 and 5, 4 and 9 in pairs are the same.

Examples

			a(2)=81 hence a(3) = 841 the smallest square formed from 81.

Links

Crossrefs

Cf. A068175, A068176, A068177, A068178, A068616.

Formula

For n>=4, a(n) = 38416*100^(n-4).
From Chai Wah Wu, Aug 03 2020: (Start)
a(n) = 100*a(n-1) for n > 4.
G.f.: x*(45684*x^3 + 7259*x^2 + 719*x - 8)/(100*x - 1). (End)

Extensions

More terms from Sean A. Irvine, Sep 24 2009
Edited and extended by Max Alekseyev, Oct 12 2009
Showing 1-7 of 7 results.

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