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 1-10 of 16 results. Next

A262532 Minimal nested palindromic primes with seed 00000.

Original entry on oeis.org

140000041, 31400000413, 9314000004139, 74931400000413947, 3749314000004139473, 937493140000041394739, 3693749314000004139473963, 10369374931400000413947396301, 351036937493140000041394739630153, 7035103693749314000004139473963015307
Offset: 2

Views

Author

Clark Kimberling, Sep 24 2015

Keywords

Comments

Let s be a palindrome and put a(1) = s. Let a(2) be the least palindromic prime having s in the middle; for n > 2, let a(n) be the least palindromic prime having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s. (For A252532, the seed is not an integer, so that the offset is 2.)

Examples

			As a triangle:
          00000
        140000041
       31400000413
      9314000004139
    74931400000413947
   3749314000004139473
  937493140000041394739

Links

Crossrefs

Cf. A261881.

Programs

  • Mathematica
    s0 = "00000"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
(* Peter J. C. Moses, Sep 23 2015 *)

A252525 Number of (n+2)X(1+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

750, 595, 460, 535, 546, 649, 823, 1036, 1328, 1756, 2254, 2949, 3882, 5007, 6535, 8608, 11078, 14439, 18930, 24343, 31630, 41368, 53110, 68859, 89778, 115127, 148930, 193720, 248118, 320379, 415794, 532023, 685810, 888376, 1135670, 1461819
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Comments

Column 1 of A252532

Examples

			Some solutions for n=4
..0..3..3....2..3..2....3..2..2....3..3..1....0..2..0....3..3..0....2..1..3
..2..3..2....2..2..3....3..0..0....3..2..2....3..2..1....1..0..1....2..0..0
..3..3..0....1..3..3....2..2..3....2..3..2....2..0..0....1..1..0....1..0..1
..3..2..2....2..3..2....3..2..2....3..3..0....0..3..3....2..0..0....1..1..0
..2..3..2....2..2..3....3..0..3....3..2..2....2..2..2....1..0..1....3..0..0
..3..3..1....1..3..3....2..2..3....2..3..2....3..0..0....1..1..0....1..0..1

Links

Formula

Empirical: a(n) = 4*a(n-3) -3*a(n-6) -4*a(n-9) +4*a(n-12) for n>23

A252526 Number of (n+2) X (2+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

730, 337, 334, 426, 676, 964, 1344, 2312, 3336, 4800, 8464, 12304, 18048, 32288, 47136, 69888, 126016, 184384, 274944, 497792, 729216, 1090560, 1978624, 2900224, 4343808, 7889408, 11567616, 17338368, 31507456, 46203904, 69279744, 125929472
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..3..1..2..3....0..2..0..0....1..0..1..1....2..0..0..3....2..3..2..2
..3..1..3..3....1..1..0..1....2..1..0..1....1..0..1..1....1..2..3..2
..2..2..3..2....0..1..1..0....2..0..0..2....1..1..0..1....1..3..3..1
..3..2..2..3....0..2..0..0....1..0..1..1....2..0..0..2....2..3..2..2
..3..0..3..3....1..1..0..1....1..1..0..1....1..0..1..2....2..2..3..1
..2..2..3..2....0..1..1..0....2..0..0..3....1..1..0..1....1..3..3..1

Links

Crossrefs

Column 2 of A252532.

Formula

Empirical: a(n) = 6*a(n-3) - 8*a(n-6) for n>10.
Empirical g.f.: x*(730 + 337*x + 334*x^2 - 3954*x^3 - 1346*x^4 - 1040*x^5 + 4628*x^6 + 952*x^7 + 224*x^8 + 144*x^9) / ((1 - 2*x^3)*(1 - 4*x^3)). - Colin Barker, Dec 04 2018

A252527 Number of (n+2) X (3+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

621, 341, 466, 610, 1114, 1748, 2332, 4244, 6760, 9112, 16552, 26576, 36016, 65360, 105376, 143200, 259744, 419648, 571072, 1035584, 1674880, 2280832, 4135552, 6692096, 9116416, 16528640, 26753536, 36451840, 66087424, 106984448, 145779712
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..3..0..3..0..0....3..0..3..3..0....3..2..2..3..2....3..0..3..3..0
..2..2..3..2..2....2..2..3..2..2....3..0..3..3..1....2..2..3..2..2
..3..2..2..3..2....3..2..2..3..2....2..2..3..2..2....3..2..2..3..2
..3..0..3..3..1....3..1..3..3..1....3..2..2..3..2....3..0..3..3..0
..2..2..3..2..1....2..2..3..2..2....3..1..3..3..0....2..2..3..2..2
..3..2..2..3..2....3..2..2..3..1....2..2..3..2..2....3..2..2..3..2

Links

Crossrefs

Column 3 of A252532.

Formula

Empirical: a(n) = 6*a(n-3) - 8*a(n-6) for n>8.
Empirical g.f.: x*(621 + 341*x + 466*x^2 - 3116*x^3 - 932*x^4 - 1048*x^5 + 3640*x^6 + 288*x^7) / ((1 - 2*x^3)*(1 - 4*x^3)). - Colin Barker, Dec 04 2018

A252528 Number of (n+2) X (4+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

719, 462, 626, 790, 1676, 2504, 3160, 6704, 10016, 12640, 26816, 40064, 50560, 107264, 160256, 202240, 429056, 641024, 808960, 1716224, 2564096, 3235840, 6864896, 10256384, 12943360, 27459584, 41025536, 51773440, 109838336
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..0..2..0..0..3..0....3..1..3..3..1..3....2..1..0..1..1..0....3..0..3..3..0..3
..1..1..0..1..1..0....2..2..3..2..2..3....2..0..0..3..0..3....2..2..3..2..2..3
..0..1..1..0..1..1....3..2..2..3..2..2....1..0..1..1..0..1....3..2..2..3..2..2
..0..2..0..0..2..0....3..1..3..3..1..3....1..1..0..1..1..0....3..0..3..3..0..3
..1..1..0..1..1..0....2..2..3..2..2..3....3..0..0..3..0..0....2..2..3..2..2..3
..0..1..1..0..1..1....3..2..2..3..1..2....1..0..1..1..0..1....3..2..2..3..2..2

Links

Crossrefs

Column 4 of A252532.

Formula

Empirical: a(n) = 4*a(n-3) for n>5.
Empirical g.f.: x*(719 + 462*x + 626*x^2 - 2086*x^3 - 172*x^4) / (1 - 4*x^3). - Colin Barker, Dec 04 2018

A252529 Number of (n+2) X (5+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

778, 706, 1120, 1592, 4420, 7136, 10720, 30752, 49792, 77696, 227584, 369152, 589312, 1746944, 2836480, 4585472, 13680640, 22224896, 36167680, 108265472, 175931392, 287277056, 861405184, 1399980032, 2289958912, 6872367104
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..3..1..3..3..1..3..3....2..0..0..2..0..0..2....1..0..1..1..0..1..1
..2..2..3..2..2..3..2....1..0..1..1..0..1..1....1..1..0..1..1..0..1
..3..2..2..3..2..2..3....1..1..0..1..1..0..1....3..0..0..3..0..0..2
..3..1..3..3..0..3..3....2..0..0..3..0..0..2....1..0..1..1..0..1..1
..2..2..3..2..2..3..2....1..0..1..1..0..1..2....1..1..0..1..1..0..1
..3..2..2..3..2..2..3....1..1..0..1..1..0..1....2..0..0..3..0..0..3

Links

Crossrefs

Column 5 of A252532.

Formula

Empirical: a(n) = 12*a(n-3) - 32*a(n-6) for n>8.
Empirical g.f.: 2*x*(389 + 353*x + 560*x^2 - 3872*x^3 - 2026*x^4 - 3152*x^5 + 8256*x^6 + 152*x^7) / ((1 - 2*x)*(1 + 2*x + 4*x^2)*(1 - 4*x^3)). - Colin Barker, Dec 04 2018

A252530 Number of (n+2) X (6+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

932, 1000, 1760, 2440, 7184, 13184, 18656, 54464, 101888, 145792, 423680, 800768, 1152512, 3341312, 6348800, 9164800, 26537984, 50561024, 73097216, 211533824, 403570688, 583892992, 1689190400, 3224895488, 4667604992, 13501202432
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..0..1..1..0..1..1..0..1....2..2..3..2..2..3..2..2....2..0..0..3..0..0..3..3
..1..0..1..1..0..1..1..0....3..2..2..3..2..2..3..2....1..0..1..1..0..1..1..0
..0..0..2..0..0..3..0..0....3..0..3..3..1..3..3..0....1..1..0..1..1..0..1..1
..0..1..1..0..1..1..0..1....2..2..3..2..2..3..2..2....3..0..0..3..0..0..3..0
..1..0..1..1..0..1..1..0....3..2..2..3..2..2..3..2....1..0..1..1..0..1..1..0
..0..0..3..0..0..2..0..0....3..0..3..3..0..3..3..0....1..1..0..1..1..0..1..1

Links

Crossrefs

Column 6 of A252532.

Formula

Empirical: a(n) = 12*a(n-3) - 32*a(n-6) for n>8.
Empirical g.f.: 4*x*(233 + 250*x + 440*x^2 - 2186*x^3 - 1204*x^4 - 1984*x^5 + 4800*x^6 + 64*x^7) / ((1 - 2*x)*(1 + 2*x + 4*x^2)*(1 - 4*x^3)). - Colin Barker, Dec 04 2018

A252531 Number of (n+2) X (7+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

1200, 1468, 2404, 3160, 11456, 19232, 25280, 91648, 153856, 202240, 733184, 1230848, 1617920, 5865472, 9846784, 12943360, 46923776, 78774272, 103546880, 375390208, 630194176, 828375040, 3003121664, 5041553408, 6627000320
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..3..2..2..3..2..2..3..2..2....1..1..0..1..1..0..1..1..0
..3..1..3..3..1..3..3..1..3....0..1..1..0..1..1..0..1..1
..2..2..3..2..2..3..2..2..3....0..3..0..0..3..0..0..3..0
..3..2..2..3..2..2..3..2..2....1..1..0..1..1..0..1..1..0
..3..0..3..3..1..3..3..0..3....0..1..1..0..1..1..0..1..1
..2..2..3..2..2..3..2..2..3....3..3..0..0..2..0..0..2..0

Links

Crossrefs

Column 7 of A252532.

Formula

Empirical: a(n) = 8*a(n-3) for n>5.
Empirical g.f.: 4*x*(300 + 367*x + 601*x^2 - 1610*x^3 - 72*x^4) / ((1 - 2*x)*(1 + 2*x + 4*x^2)). - Colin Barker, Dec 04 2018

A252533 Number of (1+2)X(n+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

750, 730, 621, 719, 778, 932, 1200, 1498, 1968, 2708, 3473, 4698, 6444, 8494, 11435, 15560, 20630, 27462, 36761, 48910, 64407, 85224, 113390, 148048, 193940, 258080, 334681, 435134, 578923, 746716, 964795, 1283490, 1648229, 2118894, 2818420
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Comments

Row 1 of A252532

Examples

			Some solutions for n=4
..2..2..2..3..1..3....3..1..3..3..1..3....3..3..0..0..0..3....1..1..0..1..1..0
..2..1..0..1..1..0....2..2..3..2..2..3....3..2..2..3..1..3....3..0..0..3..0..3
..1..2..3..1..3..2....3..2..2..3..1..2....2..3..2..1..3..2....1..0..1..1..0..1

Links

Formula

Empirical: a(n) = 4*a(n-3) -3*a(n-6) -4*a(n-9) +4*a(n-12) for n>39

A252534 Number of (2+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

Original entry on oeis.org

595, 337, 341, 462, 706, 1000, 1468, 2420, 3480, 5240, 8872, 12880, 19696, 33872, 49440, 76256, 132256, 193600, 299968, 522560, 766080, 1189760, 2077312, 3047680, 4738816, 8283392, 12157440, 18914816, 33081856, 48563200, 75578368, 132224000
Offset: 1

Views

Author

R. H. Hardin, Dec 18 2014

Keywords

Examples

			Some solutions for n=4:
..1..2..3..2..2..3....1..3..3..0..0..3....3..3..0..0..2..0....3..3..0..3..0..0
..3..2..2..3..2..2....2..3..2..2..3..2....0..0..2..0..0..2....3..2..2..3..2..2
..0..0..3..3..1..3....2..2..3..2..2..3....1..2..3..1..2..3....2..3..2..2..3..2
..2..2..3..2..2..3....0..3..3..1..3..3....0..2..0..0..3..0....0..3..0..3..3..0

Links

Crossrefs

Row 2 of A252532.

Formula

Empirical: a(n) = 6*a(n-3) - 8*a(n-6) for n>10.
Empirical g.f.: x*(595 + 337*x + 341*x^2 - 3108*x^3 - 1316*x^4 - 1046*x^5 + 3456*x^6 + 880*x^7 + 208*x^8 + 128*x^9) / ((1 - 2*x^3)*(1 - 4*x^3)). - Colin Barker, Dec 04 2018
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