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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A250257 Least nonnegative integer whose decimal digits divide the plane into n regions.

Original entry on oeis.org

1, 0, 8, 48, 88, 488, 888, 4888, 8888, 48888, 88888, 488888, 888888, 4888888, 8888888, 48888888, 88888888, 488888888, 888888888, 4888888888, 8888888888, 48888888888, 88888888888, 488888888888, 888888888888, 4888888888888, 8888888888888, 48888888888888
Offset: 1

Views

Author

Rick L. Shepherd, Nov 15 2014

Keywords

Comments

Equivalently, with offset 0, least nonnegative integer with n holes in its decimal digits. Leading zeros are not permitted. Identical to A249572 except that a(2) = 0, not 4. See also the comments in A249572.

Examples

			The integer 48, whose decimal digits have 3 holes, divides the plane into 4 regions. No smaller nonnegative integer does this, so a(4) = 48.

Links

Crossrefs

Cf. A249572, A250256, A250258, A001743, A001744, A001745, A001746, A002282.

Programs

  • Magma
    I:=[1,0,8,48,88]; [n le 5 select I[n] else 10*Self(n-2)+8: n in [1..30]]; // Vincenzo Librandi, Nov 15 2014
  • Mathematica
    Join[{1, 0, 8}, RecurrenceTable[{a[1]==48, a[2]==88, a[n]==10 a[n-2] + 8}, a, {n, 20}]] (* Vincenzo Librandi, Nov 16 2014 *)

Formula

a(n) = 10*a(n-2) + 8 for n >= 5.
From Chai Wah Wu, Jul 12 2016: (Start)
a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 5.
G.f.: x*(-40*x^4 + 50*x^3 - 2*x^2 - x + 1)/((x - 1)*(10*x^2 - 1)). (End)

A250258 Least nonnegative integer whose decimal digits divide the plane into n regions (A250257 variant).

Original entry on oeis.org

1, 0, 8, 68, 88, 688, 888, 6888, 8888, 68888, 88888, 688888, 888888, 6888888, 8888888, 68888888, 88888888, 688888888, 888888888, 6888888888, 8888888888, 68888888888, 88888888888, 688888888888, 888888888888, 6888888888888, 8888888888888, 68888888888888
Offset: 1

Views

Author

Rick L. Shepherd, Nov 15 2014

Keywords

Comments

Equivalently, with offset 0, least nonnegative integer with n holes in its decimal digits. Leading zeros are not permitted. Variation of A250257 with the numeral "4" considered open at the top, as it is often handwritten. See also the comments in A249572.

Examples

			The integer 68, whose decimal digits have 3 holes, divides the plane into 4 regions. No smaller nonnegative integer does this, so a(4) = 68.

Links

Crossrefs

Cf. A249572, A250256, A250257, A001743, A001744, A001745, A001746, A002282.

Programs

  • Magma
    I:=[1,0,8,68,88]; [n le 5 select I[n] else 10*Self(n-2)+8: n in [1..40]]; // Vincenzo Librandi, Nov 16 2014
  • Mathematica
    Join[{1, 0, 8}, RecurrenceTable[{a[1]==68, a[2]==88, a[n]==10 a[n-2] + 8}, a, {n, 20}]] (* Vincenzo Librandi, Nov 16 2014 *)

Formula

a(n) = 10*a(n-2) + 8 for n >= 5.
a(n) = A250256(n), n<>2.
From Chai Wah Wu, Jul 12 2016: (Start)
a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 5.
G.f.: x*(-60*x^4 + 70*x^3 - 2*x^2 - x + 1)/((x - 1)*(10*x^2 - 1)). (End)

A113591 Least multiple of composite(n), containing only composite digits (0,4,6,8,9).

Original entry on oeis.org

0, 4, 6, 8, 9, 40, 48, 84, 60, 48, 90, 40, 84, 44, 48, 400, 468, 486, 84, 60, 64, 66, 68, 490, 468, 494, 468, 40, 84, 44, 90, 46, 48, 49, 400, 408, 468, 486, 440, 448, 684, 406, 60, 496, 6048, 64, 4680, 66, 68, 69, 490, 648, 444, 600, 608, 4004, 468, 80, 486, 984, 84
Offset: 0

Views

Author

Amarnath Murthy, Nov 07 2005

Keywords

Comments

The sequence A002808 is extended with A002808(0)=0 to define "composite" here. Every term occurs in A001744. - R. J. Mathar, Aug 28 2007

Examples

			a(7) = 84, composite (7) =14, term corresponding to 14 is 84.

Crossrefs

Cf. A002808, A078240, A113590.

Formula

a(n) = A078240(A002808(n)) for n > 0. - Andrew Howroyd, Sep 17 2024

Extensions

Corrected and extended by R. J. Mathar, Aug 28 2007

A113624 7-smooth numbers containing only composite digits (0,4,6,8,9).

Original entry on oeis.org

4, 6, 8, 9, 40, 48, 49, 60, 64, 80, 84, 90, 96, 98, 400, 448, 480, 486, 490, 600, 640, 648, 686, 800, 840, 864, 896, 900, 960, 980, 4000, 4096, 4480, 4608, 4800, 4860, 4900, 6000, 6048, 6400, 6480, 6804, 6860, 8000, 8064, 8400, 8640, 8960, 9000, 9408, 9600
Offset: 1

Views

Author

Amarnath Murthy, Nov 10 2005

Keywords

Examples

			96 is a term as 96 = 2^5*3 and contains digits 9,6 both composite. 96 is a member of A002473.

Crossrefs

Intersection of A001744 and A002473.
Cf. A113623.

Programs

  • Mathematica
    Select[Select[Range[2, 10000], FactorInteger[ # ][[ -1]][[1]] <= 7 &], DigitCount[ # ][[1]]+DigitCount[ # ][[2]]+DigitCount[ # ][[3]]+DigitCount[ # ][[5]]+ DigitCount[ # ][[7]] == 0 &] (* Stefan Steinerberger, Apr 11 2006 *)

Extensions

More terms from Stefan Steinerberger, Apr 11 2006
Name corrected and offset changed by Andrew Howroyd, Sep 17 2024

A261449 Prime numbers whose decimal digits contain a total of two loops.

Original entry on oeis.org

83, 109, 149, 181, 199, 269, 281, 283, 349, 383, 401, 419, 439, 443, 461, 463, 467, 479, 491, 509, 569, 587, 599, 601, 607, 619, 641, 643, 647, 659, 661, 691, 709, 769, 787, 811, 821, 823, 827, 853, 857, 877, 907, 919, 929, 941, 947, 967, 991, 997, 1019, 1039
Offset: 1

Views

Author

Altug Alkan, Aug 19 2015

Keywords

Comments

Of the digits, 0 through 9, {0, 4, 6, 9} have one loop, 8 has two loops, and all the rest have none. - Robert G. Wilson v, Aug 20 2015

Examples

			83 is the first term of the sequence. The digit 8 contains two closed curves.

Crossrefs

Cf. A001729, A190222, A001743, A001744, A001745, A249572.

Programs

  • Mathematica
    Select[Prime@ Range@ 200, 2 == Total[{ 1,0, 0,0, 1,0, 1,0, 2,1}[[1 + IntegerDigits@ #]]]&] (* Giovanni Resta, Aug 19 2015 *)

Extensions

More terms from Giovanni Resta, Aug 19 2015
Previous Showing 21-25 of 25 results.

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