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 1-9 of 9 results.

A158024 Primes p such that all the digits needed to write the consecutive Primes from 2 to p fill exactly a square (no holes, no overlaps).

Original entry on oeis.org

2, 7, 29, 71, 101, 127, 191, 229, 317, 379, 499, 577, 733, 823, 10867, 11159, 12301, 12577, 13781, 14107, 15391, 15733, 17183, 17509, 19079, 19457, 21023, 21467, 23059, 23549, 25339, 25793, 27733, 28151, 30161, 30697, 32719, 33247, 35401
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The sides of the successive squares are given by A158025. Terms computed by Jean-Marc Falcoz.

Examples

			...2...23...2357
.......57...1113
............1719
............2329
The primes fitting exactly in the SE corner of the above squares are 2, 7, 29. There is no 3X3 square where this is possible.

Links

Programs

  • Maple
    X:= 0: p:= 1:
Res:= NULL: count:= 0:
while count < 100 do
  p:= nextprime(p);
  X:= X + ilog10(p) + 1;
  if issqr(X) then Res:= Res,p; count:= count+1 fi
od:
Res; # Robert Israel, Jan 13 2020

A158025 Sides of squares which are filled exactly (no holes, no overlaps) by the digits needed to write a subsequence of consecutive Primes starting with 2.

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 72, 73, 77, 78, 82, 83, 87, 88, 92, 93, 97, 98, 102, 103, 107, 108, 112, 113, 117, 118, 122, 123, 127, 128, 132, 133, 137, 138, 142, 143, 147, 148, 152, 153, 157, 158, 162, 163, 167, 168, 172, 173, 177, 178, 182, 183
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The primes fitting exactly in a "Primes-digits square" are given by A158024. Terms computed by Jean-Marc Falcoz.

Examples

			...2...23...2357
.......57...1113
............1719
............2329
The above squares, filled exactly by a subsequence of consecutive primes starting with 2 have sides 1, 2, 4. There is no side-3 square with this property. The next properly filled square will have side 6.

Links

Programs

  • Maple
    X:= 0: p:= 1:
Res:= NULL: count:= 0:
while count < 100 do
  p:= nextprime(p);
  X:= X + ilog10(p) + 1;
  if issqr(X) then Res:= Res,sqrt(X); count:= count+1: fi
od:
Res; # Robert Israel, Jan 13 2020

A158023 Sides of squares which are filled exactly (no holes, no overlaps) by the digits needed to write a subsequence of consecutive nonnegative integers starting with 0.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The integers fitting exactly in a "nonnegative-integers-digits square" are given by A158022. Terms computed by Jean-Marc Falcoz.

Examples

			...0...01...012...0123...012345
.......23...345...4567...678910
............678...8910...111213
..................1112...141516
.........................171819
.........................202122
The above squares, filled exactly by a subsequence of nonnegative integers starting with 0, have sides 1, 2, 3, 4, 6. There is no side-5 square with this property. The next properly filled square will have side 6.

Links

Crossrefs

Cf. A158022.

A158026 Fibonacci numbers f such that all the digits needed to write the consecutive Fibonacci numbers from 0 to f fill exactly a square (no holes, no overlaps).

Original entry on oeis.org

0, 2, 13, 1597, 1134903170, 3416454622906707, 10284720757613717413913, 394810887814999156320699623170776339
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The sides of the successive squares are given by A158027. Terms computed by Jean-Marc Falcoz.

Examples

			...0...01...011...011235
.......12...235...813213
............813...455891
..................442333
..................776109
..................871597
The Fibonacci numbers fitting exactly in the SE corner of the above squares are 0, 2, 13, 1597. There are no 4x4 or 5x5 squares where this is possible.

Links

A158027 Sides of squares which are filled exactly (no holes, no overlaps) by the digits needed to write a subsequence of consecutive Fibonacci numbers, starting with 0.

Original entry on oeis.org

1, 2, 3, 6, 15, 25, 35, 56, 227, 398, 847, 986, 1713, 4589, 6460, 7465, 24860, 28741
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The Fibonacci numbers fitting exactly in a "Fibonacci-digits square" are given by A158026. Terms computed by Jean-Marc Falcoz.

Examples

			...0...01...011...011235
.......12...235...813213
............813...455891
..................442333
..................776109
..................871597
The above squares, filled exactly by a subsequence of consecutive Fibonacci numbers starting with 0 have sides 1, 2, 3, 6. There are no side-4 and side-5 squares with this property. The next properly filled square will have side 15.

Links

A158028 Square numbers s such that all the digits needed to write the consecutive square numbers from 0 to s fill exactly a square (no holes, no overlaps).

Original entry on oeis.org

0, 9, 81, 144, 400, 625, 15625, 17956, 30276, 34225, 54289, 60516, 91204, 1113025, 1478656, 1934881, 2496400, 3179089, 4000000, 4977361, 6130576, 7480225, 9048064, 1009205824, 1063281664, 1077152400, 1134072976, 1148667664
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The sides of the successive squares are given by A158029. Terms computed by Jean-Marc Falcoz.

Examples

			...0...01...0116...01161
.......49...4964...49640
............2539...25390
............6481...64811
...................21144
The square numbers fitting exactly in the SE corner of the above squares are 0, 9, 81, 144. There is no 3x3 square where this is possible.

Links

A158029 Sides of squares which are filled exactly (no holes, no overlaps) by the digits needed to write a subsequence of consecutive square numbers, starting with 0.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 22, 23, 27, 28, 32, 33, 37, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 521, 529, 531, 539, 541, 549, 551, 559, 561, 569, 571, 579, 581, 589, 591, 599, 601, 609, 611, 619, 621, 629, 631, 639, 641, 649, 651, 659, 661, 669, 671
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The square numbers fitting exactly in a "squares-digits square" are given by A158028. Terms computed by Jean-Marc Falcoz.

Examples

			...0...01...0116...01161
.......49...4964...49640
............2539...25390
............6481...64811
...................21144
The above squares, filled exactly by a subsequence of consecutive square numbers starting with 0 have sides 1, 2, 4, 5. There is no side-3 square with this property. The next properly filled square will have side 7.

Links

A158030 Triangular numbers t such that all the digits needed to write the consecutive triangular numbers from 0 to t fill exactly an equilateral triangle (no holes, no overlaps).

Original entry on oeis.org

0, 3, 10, 21, 153, 210, 378, 496, 820, 1431, 3081, 4656, 8646, 11628, 15051, 17766, 22578, 26335, 32896, 37950, 46665, 53301, 64620, 73153, 87571, 98346, 108345, 113526, 130305, 162735, 185136, 193131, 218791, 267546, 300700, 312445, 349866
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The sides of the successive triangles are given by A158031. Terms computed by Jean-Marc Falcoz.

Examples

			...0....0....0.....0
........13...13....13
.............610...610
...................1521
The triangular numbers fitting exactly in the SE corner of the above triangles are 0, 3, 10, 21.

Links

A158031 Sides of equilateral triangles which are filled exactly (no holes, no overlaps) by the digits used to write a subsequence of consecutive triangular numbers, starting with 0.

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 11, 12, 14, 17, 22, 25, 30, 33, 36, 38, 41, 43, 46, 48, 51, 53, 56, 58, 61, 63, 65, 66, 69, 74, 77, 78, 81, 86, 89, 90, 93, 98, 101, 102, 105, 110, 113, 114, 117, 122, 125, 126, 132, 133, 139, 140, 146, 147, 153, 154, 160, 161, 167, 168, 174, 175, 181
Offset: 1

Views

Author

Eric Angelini, Mar 11 2009

Keywords

Comments

The triangular numbers fitting exactly in a "triangulars-digits triangle" are given by A158030. Terms computed by Jean-Marc Falcoz.

Examples

			...0....0....0.....0
........13...13....13
.............610...610
...................1521
The above "equilateral" triangles, filled exactly by a subsequence of consecutive triangular numbers starting with 0 have sides 1, 2, 3, 4. The next properly filled triangle will have side 8.

Links

Showing 1-9 of 9 results.

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