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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

%I

%S 1,31,313,1313,13131,313131,3131313,13131313,131313131,3131313131,

%T 31313131313,131313131313,1313131313131,31313131313131,

%U 313131313131313,1313131313131313,13131313131313131,313131313131313131

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

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

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

%F 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

%F 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

%p 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

%Y Cf. A000040, A000042.

%K nonn,base,easy

%O 1,2

%A _Ctibor O. Zizka_, Apr 06 2008

%E More terms from _R. J. Mathar_, Apr 09 2008

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Last modified December 6 19:31 EST 2019. Contains 329809 sequences. (Running on oeis4.)