|
Search: id:A137318
|
|
|
| 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
|
|
| 1, 31, 313, 1313, 13131, 313131, 3131313, 13131313, 131313131, 3131313131, 31313131313, 131313131313, 1313131313131, 31313131313131, 313131313131313, 1313131313131313, 13131313131313131, 313131313131313131
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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...
|
|
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 (mathar(AT)strw.leidenuniv.nl), 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 (ppl(AT)spl.at), 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 (ppl(AT)spl.at), Apr 15 2008
|
|
CROSSREFS
|
Cf. A000040, A000042.
Adjacent sequences: A137315 A137316 A137317 this_sequence A137319 A137320 A137321
Sequence in context: A126552 A068813 A142382 this_sequence A029813 A138697 A033175
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Apr 06 2008
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008
|
|
|
Search completed in 0.002 seconds
|
