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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.

User: Lynn R. Purser

Lynn R. Purser's wiki page.

Lynn R. Purser has authored 2 sequences.

A226251 Period 10: repeat [1, 1, 2, 3, 5, 8, 1, 3, 4, 7].

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7, 1, 1, 2, 3, 5, 8, 1, 3, 4, 7
Offset: 1

Views

Author

Lynn R. Purser, Jun 03 2013

Keywords

Comments

Previous name was: Concatenated cyclical sequence starting from Fibonacci sequence.
Start with the Fibonacci sequence 0,1,1,2,3,5,8; at this point rewrite the next term 13 as 1,3 and continue adding: 1,3,4,7. At this point rewrite the sum 11 as 1,1 and the sequence will recur if values greater than or equal to 10 are rewritten as two single-digit values as 0,1,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1,1,...

Examples

			1) (9,9) 9,9,1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1, 1, 2, 3, 5, 8, 1, 3, 4, 7, ...
2) (3,7) 3,7,9,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1, 1, 2, 3, 5, 8, 1, 3, 4, 7, ...
3) (0,4) 0,4,4,8,1,2,3,5,8,1,3,4,7,1,1,2,3,5,8,1,3,4,7,1, 1, 2, 3, 5, 8, 1, 3, 4, 7, ...
However if the sequence starts with one of the following, (0,7),(1,4),(2,6),(3,1),(4,2),(4,5),(5,9),(6,8),(7,0),(7,7),(8,6),(9,5) the sequence converges to 1,4,5,9 which is listed as a subsequence of A000285. For all but the trivial exception (0,0) the rest of the two-digit combinations when added together will generate the sequence.

Links

Programs

  • Mathematica
    nxt[{a_,b_}]:=If[b>9,IntegerDigits[b],{b,a+b}]; NestList[nxt,{1,1},120][[All,1]] (* Harvey P. Dale, Jan 07 2020 *)
PadRight[{},120,{1,1,2,3,5,8,1,3,4,7}] (* Harvey P. Dale, Jan 07 2020 *)

Extensions

More terms from Harvey P. Dale, Jan 07 2020
New name from Joerg Arndt, May 29 2025

A119408 Decimal equivalent of the binary string generated by the n X n identity matrix.

Original entry on oeis.org

1, 9, 273, 33825, 17043521, 34630287489, 282578800148737, 9241421688590303745, 1210107565283851686118401, 634134936313486520338360567809, 1329552593586084350528447794605199361, 11151733894906779683522195341810241573494785
Offset: 1

Views

Author

Lynn R. Purser, Jul 25 2006

Keywords

Comments

a(n) is divisible by 2^n - 1. a(n) == n mod 2^(n+1) - 1. - Robert Israel, Jun 09 2015

Examples

			n=2: [1 0; 0 1] == 1001_2 = 9;
n=3: [1 0 0; 0 1 0; 0 0 1] == 100010001_2 = 273;
n=4: [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1] == 1000010000100001_2 = 33825.

Links

Crossrefs

Cf. A128889.

Programs

  • MATLAB
    for n = 1:10 bi2de((reshape(eye(n),length(eye(n))^2,1))') end
% Kyle Stern, Dec 14 2011
  • Mathematica
    For[n=2,n<=10,Print[n," ",Sum[2^((n+1)(k-1)), {k,1,n}]];n++ ]
Table[FromDigits[Flatten[IdentityMatrix[n]],2],{n,15}] (* Harvey P. Dale, Dec 31 2021 *)
  • PARI
    a(n)=(2^n*2^(n^2)-1)/(2*2^n-1) \\ Charles R Greathouse IV, Jun 09 2015

Formula

a(n) = 2^((n+1)(n-1)) + 2^((n+1)(n-2)) + ... + 1 where n=2,3,...
a(n) = (2^n*2^(n^2)-1)/(2*2^n-1). - Stuart Bruff, Jun 08 2015

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