login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137318 Concatenation of segments of the digit sequence 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3.... 0
1, 31, 313, 1313, 13131, 313131, 3131313, 13131313, 131313131, 3131313131, 31313131313, 131313131313, 1313131313131, 31313131313131, 313131313131313, 1313131313131313, 13131313131313131, 313131313131313131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A000042 is 1,11,111,1111,11111,... concatenation of 111111111111111....

A002276 is 2,22,222,2222,22222,... concatenation of 222222222222222....

A133013 is 2,35,71113,... concatenation of 2 3 5 7 11 13 17 19 23 29,...

LINKS

Table of n, a(n) for n=1..18.

FORMULA

O.g.f.: x*(100x^4 + 200x^3 + 83x^2 + 20x + 1)/((10x-1)(100x^2+1)(x-1)(x^2+1)). - R. J. Mathar, Apr 09 2008

a(n+1) = (1/4)*((n mod 4) + ((n+1) mod 4) + ((n+2) mod 4) - ((n+3) mod 4))*(10^n)*(1+(-1)^(n+1)) + a(n)*10^(1/2 + 1/2*(-1)^n) + (1/4)*((n mod 4) + ((n+1) mod 4) - ((n+2) mod 4) + ((n+3) mod 4))*(1+(-1)^n), with a(0)=1 and n >= 1. - Paolo P. Lava, Apr 15 2008

MAPLE

P:=proc(n) local a, i; a:=1; print(a); for i from 1 by 1 to n do a:=(1/4*((i mod 4)+((i+1) mod 4)+((i+2) mod 4)-((i+3) mod 4)))*(10^i)*(1+(-1)^(i+1))+a*10^((1/2+1/2*(-1)^(i)))+(1/4*((i mod 4)+((i+1) mod 4)-((i+2) mod 4)+((i+3) mod 4)))*(1+(-1)^(i)); print(a); od; end: P(100); # Paolo P. Lava, Apr 15 2008

CROSSREFS

Cf. A000040, A000042.

Sequence in context: A068813 A221306 A142382 * A182025 A221189 A029813

Adjacent sequences:  A137315 A137316 A137317 * A137319 A137320 A137321

KEYWORD

nonn,base,easy

AUTHOR

Ctibor O. Zizka, Apr 06 2008

EXTENSIONS

More terms from R. J. Mathar, Apr 09 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)