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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A022501 Describe the previous term! (method B - initial term is 5).

Original entry on oeis.org

5, 51, 5111, 5113, 511231, 5112213111, 511222113113, 51122312311231, 5112223111213112213111, 51122331132111311222113113, 511222321231211331122312311231
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Method B = 'digit'-indication followed by 'frequency'.

Examples

			E.g. the term after 5113 is obtained by saying "5 once, 1 twice, 3 once", which gives 511231.

Links

Crossrefs

Cf. A007651, A022470, A022499, A022500-A022505.

Extensions

Typo in data correct by Peter J. C. Moses, Jun 14 2013

A022502 Describe the previous term! (method B - initial term is 6).

Original entry on oeis.org

6, 61, 6111, 6113, 611231, 6112213111, 611222113113, 61122312311231, 6112223111213112213111, 61122331132111311222113113, 611222321231211331122312311231
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Method B = 'digit'-indication followed by 'frequency'.

Examples

			E.g. the term after 6113 is obtained by saying "6 once, 1 twice, 3 once", which gives 611231.

Links

Crossrefs

Cf. A007651, A022470, A022499, A022500-A022505.

A022503 Describe the previous term! (method B - initial term is 7).

Original entry on oeis.org

7, 71, 7111, 7113, 711231, 7112213111, 711222113113, 71122312311231, 7112223111213112213111, 71122331132111311222113113, 711222321231211331122312311231
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Method B = 'digit'-indication followed by 'frequency'.

Examples

			E.g. the term after 7113 is obtained by saying "7 once, 1 twice, 3 once", which gives 711231.

Links

Crossrefs

Cf. A007651, A022470, A022499, A022500-A022505.

A022504 Describe the previous term! (method B - initial term is 8).

Original entry on oeis.org

8, 81, 8111, 8113, 811231, 8112213111, 811222113113, 81122312311231, 8112223111213112213111, 81122331132111311222113113, 811222321231211331122312311231
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Method B = 'digit'-indication followed by 'frequency'.

Examples

			E.g. the term after 8113 is obtained by saying "8 once, 1 twice, 3 once", which gives 811231.

Links

Crossrefs

Cf. A007651, A022470, A022499, A022500-A022505.

A120964 An infinite audioactive word, one of four in the cycle that results from the limit of the 'Look and Say' sequence using method B with an initial term of 1.

Original entry on oeis.org

1, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 2, 1, 3, 3, 1, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 1, 3, 1, 1, 3, 2, 1, 1, 2, 3, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 3, 1, 2, 1, 1, 3, 3, 1, 1, 2, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 1, 3
Offset: 1

Views

Author

Franklin T. Adams-Watters, Jul 19 2006

Keywords

Comments

Look and say once generates A120965, the second iteration generates A120966, the third gives A120967 and the fourth iteration returns to this sequence.

Crossrefs

Cf. A007651, A120965, A120966, A120967.

A120965 An infinite audioactive word, one of four in the cycle that results from the limit of the 'Look and Say' sequence using method B with an initial term of 1.

Original entry on oeis.org

1, 2, 2, 2, 1, 2, 3, 1, 1, 2, 2, 3, 1, 1, 3, 2, 1, 2, 2, 3, 3, 1, 2, 1, 1, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 1, 3, 1, 1, 1, 2, 2, 3, 1, 1, 3, 2, 1, 1, 2, 2, 3, 1, 1, 2, 2, 1, 1, 3, 1, 1, 3, 2, 1, 1, 2, 3, 2, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 2, 2, 2, 3, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 1, 3
Offset: 1

Views

Author

Franklin T. Adams-Watters, Jul 19 2006

Keywords

Comments

Look and say once generates A120966, the second iteration generates A120967, the third gives A120964 and the fourth iteration returns to this sequence.

Crossrefs

Cf. A007651, A120964, A120966, A120967.

A120966 An infinite audioactive word, one of four in the cycle that results from the limit of the 'Look and Say' sequence using method B with an initial term of 1.

Original entry on oeis.org

1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 1, 2, 2, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 1, 2, 2, 3, 2, 1, 1, 2, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 3, 2, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 2, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 1, 2
Offset: 1

Views

Author

Franklin T. Adams-Watters, Jul 19 2006

Keywords

Comments

Look and say once generates A120967, the second iteration generates A120964, the third gives A120965 and the fourth iteration returns to this sequence.

Crossrefs

Cf. A007651, A120964, A120965, A120967.

A120967 An infinite audioactive word, one of four in the cycle that results from the limit of the 'Look and Say' sequence using method B with an initial term of 1.

Original entry on oeis.org

1, 2, 2, 1, 3, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 3, 2, 1, 1, 2, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 2, 2, 3, 1, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1
Offset: 1

Views

Author

Franklin T. Adams-Watters, Jul 19 2006

Keywords

Comments

Look and say once generates A120964, the second iteration generates A120965, the third gives A120966 and the fourth iteration returns to this sequence.

Crossrefs

Cf. A007651, A120964, A120965, A120966.

A127175 Primes whose "Look And Say" descriptions from left to right (in the sense of method B, i.e., digit-indication followed by frequency) are also primes.

Original entry on oeis.org

3, 7, 17, 23, 41, 89, 113, 131, 137, 163, 179, 193, 271, 281, 283, 337, 389, 431, 443, 457, 479, 587, 593, 613, 661, 673, 683, 691, 727, 739, 757, 787, 809, 829, 863, 883, 907, 983, 1009, 1051, 1087, 1123, 1153, 1163, 1181, 1213, 1229, 1249, 1279, 1297
Offset: 1

Views

Author

Lekraj Beedassy, Jan 07 2007

Keywords

Examples

			41, 337, 809, 1123, for instance, are in the sequence because their respective descriptions 4111 (4 once, 1 once), 3271 (3 twice, 7 once), 810191 (8 once, 0 once, 9 once), 122131 (1 twice, 2 once, 3 once) are also primes.

Crossrefs

Cf. A007651, A056815, A127176.

Programs

  • Mathematica
    LookAndSayB[ n_] := FromDigits@Flatten@((Through[ {First, Length}[ # ] ] &) /@ Split@IntegerDigits@n); Select[Prime@Range[215], PrimeQ@LookAndSayB@# &] (* Ray Chandler, Jan 08 2007 *)

Extensions

Corrected by Ray Chandler, Jan 08 2007

A320890 a(1) = 11. For all subsequent terms a(n), take a(n-1) and substitute for the k-th digit the binary number of times that digit has appeared in a(n-1), reading left to right from the 1st to k-th digit.

Original entry on oeis.org

11, 110, 1101, 110111, 110111100101, 11011110010111010111111001000, 1101111001011101011111100100010011010101101111011001101111011111000010001111100010010100110101011
Offset: 1

Views

Author

Thomas Anton, Oct 23 2018

Keywords

Comments

Each term is an initial segment of all of its successors.
There are always more 1's than 0's in a term.
The proportion of 0's or 1's in the n-th term approaches 1/2 as n approaches infinity.
Starting with any binary integer apart from 0 or 1 and applying the same process to yield a sequence s(n), we have that, for a sufficiently large x, a(n) is always an initial segment of s(n+x). The constancy and uniqueness of the limiting behavior of initial segments in base 2 is unique among all bases, unless the tally system is considered as a degenerate case.

Examples

			a(1) = 11
The first 1 is replaced with 1, and the second 1 is replaced with 10 (two), so a(2) = 110 (1|10)
The first 1 is replaced with 1, the second 1 with 10, and the first 0 with 1, so a(3) = 1101 (1|10|1)
The first 1 is replaced with 1, the second 1 with 10, the first 0 with 1, and the third 1 with 11 (three), so a(4) = 110111 (1|10|1|11)
The first 1 is replaced with 1, the second 1 with 10, the first 0 with 1, the third 1 with 11, the fourth 1 with 100, and the fifth 1 with 101, so a(5) = 110111100101 (1|10|1|11|100|101)
The first 1 is replaced with 1, the second 1 with 10, the first 0 with 1, the third 1 with 11, the fourth 1 with 100, the fifth 1 with 101, the sixth 1 with 110, the second 0 with 10, the third 0 with 11, the seventh 1 with 111, the fourth 0 with 100, and the eighth 1 with 1000, so a(6) = 11011110010111010111111001000 (1|10|1|11|100|101|110|10|11|111|100|1000)

Links

Crossrefs

Cf. A005150, A007651, A001387, A005151.

Programs

  • Mathematica
    FromDigits /@ Nest[Append[#, Flatten[IntegerDigits[#, 2] & /@ Table[Count[#, Last@ #] &@ #[[1 ;; k]], {k, Length@ #}]] &[#[[-1]] ] ] &, {{1, 1}}, 6] (* Michael De Vlieger, Oct 23 2018 *)
  • PARI
    eva(n) = subst(Pol(n), x, 10)
replace(v) = my(w=[], zeros=0, ones=0); for(k=1, #v, if(v[k]==0, zeros++; w=concat(w, binary(zeros))); if(v[k]==1, ones++; w=concat(w, binary(ones)))); w
terms(n) = my(v=[1, 1], i=0); while(i < n, print1(eva(v), ", "); i++; v=replace(v))
/* Print initial 7 terms as follows: */
terms(7) \\ Felix Fröhlich, Oct 23 2018
  • Python
    A320890_list = [11]
while len(A320890_list)<10:
    a0,a1,s = 0,0,''
    for d in str(A320890_list[-1]):
        if d == '0':
            a0 += 1
            s += bin(a0)[2:]
        else:
            a1 += 1
            s += bin(a1)[2:]
    A320890_list.append(int(s)) # Chai Wah Wu, Nov 30 2018
Previous Showing 11-20 of 24 results. Next

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

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