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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
 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 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

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Last modified May 18 09:14 EDT 2021. Contains 343995 sequences. (Running on oeis4.)