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 1-4 of 4 results.

A285771 Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 84", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 0, 10, 0, 100, 0, 1010, 0, 10000, 0, 101000, 0, 1000100, 0, 10101010, 0, 100000000, 0, 1010000000, 0, 10001000000, 0, 101010100000, 0, 1000000010000, 0, 10100000101000, 0, 100010001000100, 0, 1010101010101010, 0, 10000000000000000, 0, 101000000000000000
Offset: 0

Views

Author

Robert Price, Apr 25 2017

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Crossrefs

Cf. A285772, A285773, A285774.

Programs

  • Mathematica
    CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
code = 84; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

A285772 Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 84", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 0, 10, 0, 100, 0, 101000, 0, 10000, 0, 10100000, 0, 10001000000, 0, 10101010000000, 0, 100000000, 0, 101000000000, 0, 100010000000000, 0, 101010100000000000, 0, 100000001000000000000, 0, 101000001010000000000000, 0, 100010001000100000000000000, 0
Offset: 0

Views

Author

Robert Price, Apr 25 2017

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Crossrefs

Cf. A285771, A285773, A285774.

Programs

  • Mathematica
    CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
code = 84; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

A285773 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 84", based on the 5-celled von Neumann neighborhood.

Original entry on oeis.org

1, 0, 2, 0, 4, 0, 10, 0, 16, 0, 40, 0, 68, 0, 170, 0, 256, 0, 640, 0, 1088, 0, 2720, 0, 4112, 0, 10280, 0, 17476, 0, 43690, 0, 65536, 0, 163840, 0, 278528, 0, 696320, 0, 1052672, 0, 2631680, 0, 4473856, 0, 11184640, 0, 16777472, 0, 41943680, 0, 71304256, 0
Offset: 0

Views

Author

Robert Price, Apr 25 2017

Keywords

Comments

Initialized with a single black (ON) cell at stage zero.

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Crossrefs

Cf. A285771, A285772, A285774.

Programs

  • Mathematica
    CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
code = 84; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

A386019 Primes having only {0, 1, 2, 6} as digits.

Original entry on oeis.org

2, 11, 61, 101, 211, 601, 661, 1021, 1061, 1201, 1601, 1621, 2011, 2111, 2161, 2221, 2621, 6011, 6101, 6121, 6211, 6221, 6661, 10061, 10111, 10211, 10601, 11161, 11261, 11621, 12011, 12101, 12161, 12211, 12601, 12611, 16001, 16061, 16111, 16661, 20011, 20021
Offset: 1

Views

Author

Jason Bard, Jul 14 2025

Keywords

Links

Crossrefs

Supersequence of A036953, A199326, A285774.
Cf. A000040, A030430, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 6]];
  • Mathematica
    Select[FromDigits /@ Tuples[{0, 1, 2, 6}, n], PrimeQ]
  • PARI
    primes_with(, 1, [0, 1, 2, 6]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("0126"), 41))) # uses function/imports in A385776
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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