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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A138484 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 0.

Original entry on oeis.org

0, 10, 1011, 3110, 102113, 13311210, 10411223, 1322311410, 1041142322, 3213243110, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422, 2214313310, 1031331422
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

Comments

After a while sequence has period 2 -> {1031331422,2214313310}

Examples

			To get the term after 102113, we say: one 3's, three 1's, one 2's, one 0's, so 13311210.

Crossrefs

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138485-A138493.

A138493 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 9.

Original entry on oeis.org

9, 19, 1911, 3119, 192113, 13311219, 19411223, 1322311419, 1941142322, 3213243119, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422, 2214313319, 1931331422
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

Comments

After a while sequence has period 2 -> {1931331422,2214313319}

Examples

			To get the term after 192113, we say: one 3's, three 1's, one 2's, one 9's, so 13311219

Crossrefs

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484-A138492.

A014715 Decimal expansion of Conway's constant.

Original entry on oeis.org

1, 3, 0, 3, 5, 7, 7, 2, 6, 9, 0, 3, 4, 2, 9, 6, 3, 9, 1, 2, 5, 7, 0, 9, 9, 1, 1, 2, 1, 5, 2, 5, 5, 1, 8, 9, 0, 7, 3, 0, 7, 0, 2, 5, 0, 4, 6, 5, 9, 4, 0, 4, 8, 7, 5, 7, 5, 4, 8, 6, 1, 3, 9, 0, 6, 2, 8, 5, 5, 0, 8, 8, 7, 8, 5, 2, 4, 6, 1, 5, 5, 7, 1, 2, 6, 8, 1, 5, 7, 6, 6, 8, 6, 4, 4, 2, 5, 2, 2, 5, 5, 5
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

An algebraic integer of degree 71. - Charles R Greathouse IV, Aug 10 2014

Examples

			1.303577269034296391257099112152551890730702504659404875754861390628550...

References

  • John H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.
  • John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 209.
  • S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
  • Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009, page 486.
  • I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.

Links

Crossrefs

Cf. A014967, A005150, A006715, A006751.

Programs

  • Mathematica
    RealDigits[ NSolve[{0 == Plus @@ ({1, 0, -1, -2, -1, 2, 2, 1, -1, -1, -1, -1, -1, 2, 5, 3, -2, -10, -3, -2, 6, 6, 1, 9, -3, -7, -8, -8, 10, 6, 8, -5, -12, 7, -7, 7, 1, -3, 10, 1, -6, -2, -10, -3, 2, 9, -3, 14, -8, 0, -7, 9, 3, -4, -10, -7, 12, 7, 2, -12, -4, -2, 5, 0, 1, -7, 7, -4, 12, -6, 3, -6} x^Range[71, 0, -1])}, {x}, 105][[-1, -1, -1]]][[1]] (* Ryan Propper, Jul 29 2005 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 20080); x=NULL; r=solve(x=1, 2,\
x^71-x^69-2*x^68-x^67+2*x^66+2*x^65+x^64-x^63-x^62-x^61-x^60\
-x^59+2*x^58+5*x^57+3*x^56-2*x^55-10*x^54-3*x^53-2*x^52+6*x^51\
+6*x^50+x^49+9*x^48-3*x^47-7*x^46-8*x^45-8*x^44+10*x^43+6*x^42\
+8*x^41-5*x^40-12*x^39+7*x^38-7*x^37+7*x^36+x^35-3*x^34+10*x^33\
+x^32-6*x^31-2*x^30-10*x^29-3*x^28+2*x^27+9*x^26-3*x^25+14*x^24\
-8*x^23-7*x^21+9*x^20+3*x^19-4*x^18-10*x^17-7*x^16+12*x^15\
+7*x^14+2*x^13-12*x^12-4*x^11-2*x^10+5*x^9+x^7-7*x^6+7*x^5\
-4*x^4+12*x^3-6*x^2+3*x-6); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b014715.txt", n, " ", d)); } \\ Harry J. Smith, May 15 2009
  • PARI
    P=Pol([1, 0, -1, -2, -1, 2, 2, 1, -1, -1, -1, -1, -1, 2, 5, 3, -2, -10, -3, -2, 6, 6, 1, 9, -3, -7, -8, -8, 10, 6, 8, -5, -12, 7, -7, 7, 1, -3, 10, 1, -6, -2, -10, -3, 2, 9, -3, 14, -8, 0, -7, 9, 3, -4, -10, -7, 12, 7, 2, -12, -4, -2, 5, 0, 1, -7, 7, -4, 12, -6, 3, -6]); polrootsreal(P)[3] \\ Charles R Greathouse IV, Aug 10 2014

Extensions

More terms from Eric W. Weisstein, Jul 01 2003

A049064 Describe the previous term in binary (method A - initial term is 0).

Original entry on oeis.org

0, 10, 1110, 11110, 100110, 1110010110, 111100111010110, 100110011110111010110, 1110010110010011011110111010110, 1111001110101100111001011010011011110111010110, 1001100111101110101100111100111010110111001011010011011110111010110
Offset: 1

Views

Author

Olivier de Mouzon

Keywords

Comments

Method A = 'frequency' (in binary mode) followed by 'digit'-indication.
The number of digits of a(n) is A001609(n) except for n = 2. See the link from T. Sillke below. - Jianing Song, Mar 16 2019

Examples

			E.g., the term after 11110 is obtained by saying "four (i.e., 100 in binary mode) 1, one 0", which gives 100110.

Links

Crossrefs

Cf. A001387 (initial term is 1), A001391, A001609 (number of digits), A259710 (written in decimal).
Decimal look-and-say sequences: A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001151, A001154.

Formula

a(n) = A001391(n-1), n > 1. - R. J. Mathar, Oct 15 2008

Extensions

Edited by Charles R Greathouse IV, Apr 06 2010
a(11) from Kade Robertson, Jun 24 2015
Offset corrected by Jianing Song, Mar 16 2019

A088204 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=3.

Original entry on oeis.org

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

Views

Author

Paul D. Hanna, Sep 22 2003

Keywords

Comments

The sequence is obtained continuously by applying the look-and-say rule from seed 3 : 3 -> 1,3 -> 1,1,1,3 -> etc. The sequence is then determined by pairs of digits. Terms of even ranks are counts while odd ranks are figures. A225224 and A221646 are from seed 1 and A088203 from seed 2. [Jean-Christophe Hervé, May 07 2013]

Crossrefs

Cf. A088203, A087282, A005150, A006715.
Cf. A225224, A221646 (seed one).

A022471 Length of n-th term of A022470.

Original entry on oeis.org

1, 2, 4, 4, 6, 10, 12, 14, 22, 26, 30, 44, 56, 70, 98, 130, 162, 216, 292, 358, 470, 628, 792, 1050, 1384, 1788, 2334, 3072, 3974, 5162, 6784, 8786, 11420, 14992, 19484, 25388, 33160, 43262, 56252, 73392, 95798, 124496, 162556, 212048, 275976, 360154
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

a(n) is the length of the n-th term of many sequences generated by methods A and B, including those shown here:
Method A, 1st term ... Method B, 1st term
A001155, 0
A006751, 2 ......... A022470, 2
A006715, 3 ......... A022499, 3
A001140, 4 ......... A022500, 4
A001141, 5 ......... A022501, 5
A001143, 6 ......... A022502, 6
A001145, 7 ......... A022503, 7
A001151, 8 ......... A022504, 8
A001154, 9 ......... A022505, 9
Clark Kimberling, Jun 14 2013

Links

Crossrefs

Cf. A022470.

Programs

  • Mathematica
    a[0] = 2; a[n_] := a[n] = FromDigits[Flatten[{First[#], Length[#]} & /@   Split[IntegerDigits[a[n - 1]]]]]; Map[Length[IntegerDigits[a[#]]] &, Range[0, 40]] (* Peter J. C. Moses, Jun 14 2013 *)
p = {9, -9, 6, -16, 5, 2, 0, -9, -1, -1, 20, 2, 6, -3, -15, -13, 15, 20, 15, -26, -28, 7, 6, 26, -27, -4, 9, -15, 3, 2, 8, 43, 9, -39, -24, -2, -24, 28, 9, 13, 13, -18, -12, -16, 14, 13, 16, 8, -36, 1, -6, -8, 15, 1, 14, 3, -6, -7, -3, 2, -2, 2, 2, 0, -1, -2, -1, 3, 3, -1, -1, -1}; q = {-6, 9, -9, 18, -16, 11, -14, 8, -1, 5, -7, -2, -8, 14, 5, 5, -19, -3, 6, 7, 6, -16, 7, -8, 22, -17, 12, -7, -5, -7, 8, -4, 7, 9, -13, 4, 6, -14, 14, -19, 7, 13, -2, 4, -18, 0, 1, 4, 12, -8, 5, 0, -8, -1, -7, 8, 5, 2, -3, -3, 0, 0, 0, 0, 2, 1, 0, -3, -1, 1, 1, 1, -1}; gf = Fold[x #1 + #2 &, 0, p]/Fold[x #1 + #2 &, 0, q]; CoefficientList[Series[gf, {x, 0, 100}], x] (* Peter J. C. Moses, Jun 16 2013 *)

A138485 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 1.

Original entry on oeis.org

1, 11, 21, 1112, 1231, 211312, 223113, 232122, 421113, 13311214, 14411223, 13223124, 14322123, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223, 23322114, 14213223
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

Comments

After a while sequence has period 2 -> {23322114,14213223}

Examples

			To get the term after 211312, we say: two 2's, three 1's, one 3's, so 223113.

Crossrefs

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484, A138486-A138493.

A138486 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 2.

Original entry on oeis.org

2, 12, 1211, 3112, 122113, 133122, 222123, 134211, 31121413, 23411412, 22312413, 23211432, 32231421, 21321423, 23321421, 21321423, 23321421, 21321423, 23321421, 21321423, 23321421, 21321423, 23321421, 21321423
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

Comments

After a while sequence has period 2 -> {21321423,23321421}

Examples

			To get the term after 122113, we say: one 3's, three 1's, two 2's, so 133122

Crossrefs

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484, A138485, A138487-A138493.

Extensions

Duplicate term 21321423 removed by Georg Fischer, Sep 18 2023

A138487 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 3.

Original entry on oeis.org

3, 13, 1311, 3113, 2321, 112213, 133122, 222123, 134211, 31121413, 23411412, 22312413, 23211432, 32231421, 21321423, 23321421, 21321423, 23321421, 21321423, 23321421, 21321423, 23321421, 21321423, 23321421, 21321423
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

Comments

After a while sequence has period 2 -> {21321423,23321421}

Examples

			To get the term after 112213, we say: one 3's, three 1's, two 2's, so 133122

Crossrefs

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484-A138486, A138488-A138493.

A138488 Say what you see in previous term, from the right, reporting total number for each digit encountered. Initial term is 4.

Original entry on oeis.org

4, 14, 1411, 3114, 142113, 13311214, 14411223, 13223124, 14322123, 23322114, 14213223, 23322114
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

Comments

After a while sequence has period 2 -> {23322114,14213223}

Examples

			To get the term after 142113, we say: one 3's, three 1's, one 2's, one 4's, so 13311214

Crossrefs

Cf. A063850, A022482, A005150, A005151, A006751, A006715, A006711, A022506-A022513, A138484-A138487, A138489-A138493.
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