%I A137318
%S A137318 1,31,313,1313,13131,313131,3131313,13131313,131313131,3131313131,
%T A137318 31313131313,131313131313,1313131313131,31313131313131,313131313131313,
%U A137318 1313131313131313,13131313131313131,313131313131313131
%N 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....
%C A137318 A000042 is 1,11,111,1111,11111,... concatenation of 111111111111111....
%C A137318 A002276 is 2,22,222,2222,22222,... concatenation of 222222222222222....
%C A137318 A133013 is 2,35,71113,... concatenation of 2 3 5 7 11 13 17 19 23 29...
%F A137318 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
%F A137318 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
%p A137318 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
%Y A137318 Cf. A000040, A000042.
%Y A137318 Sequence in context: A126552 A068813 A142382 this_sequence A029813 A138697 
               A033175
%Y A137318 Adjacent sequences: A137315 A137316 A137317 this_sequence A137319 A137320 
               A137321
%K A137318 nonn,base,easy
%O A137318 1,2
%A A137318 Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Apr 06 2008
%E A137318 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008