cp's OEIS Frontend

A215027 a(n+1) = (concatenation of n and n+1) - a(n), a(0) = 0.

%I A215027 #24 Jul 09 2025 04:34:24
%S A215027 0,1,11,12,22,23,33,34,44,45,865,146,966,247,1067,348,1168,449,1269,
%T A215027 550,1370,651,1471,752,1572,853,1673,954,1774,1055,1875,1156,1976,
%U A215027 1257,2077,1358,2178,1459,2279,1560,2380,1661,2481,1762,2582,1863,2683,1964,2784,2065,2885,2166,2986,2267,3087,2368,3188,2469,3289,2570,3390,2671,3491,2772,3592,2873,3693
%N A215027 a(n+1) = (concatenation of n and n+1) - a(n), a(0) = 0.
%C A215027 Eric Angelini defined this by saying that "a(n)+a(n+1) = concatenation of n and (n+1)".
%C A215027 An easy induction argument shows that a(n) is always positive.
%F A215027 The o.g.f. x*(1+10*x+810*x^9-720*x^10)/(1+x)/(1-x)^2 yields correct terms up to a(99), but not beyond. - _M. F. Hasler_, Aug 23 2012
%e A215027 a(100) = concat(99,100) - a(99) = 99 100 - 4590 = 94510.
%p A215027 f:=proc(i) i*10^(1+floor(evalf(log10(i+1), 10)))+i+1; end: # A001704
%p A215027 a:=proc(n) option remember; global f; if n=1 then 1 else f(n-1)-a(n-1); fi; end;
%o A215027 (PARI) A215027(n,print_all=0)={my(a=print_all & print1(0));for(n=1,n,a=(n-1)*10^#Str(n)+n-a;print_all & print1(","a));a} \\ - _M. F. Hasler_, Aug 23 2012
%Y A215027 Cf. A001704, A215028.
%K A215027 nonn,base
%O A215027 0,3
%A A215027 _N. J. A. Sloane_, Aug 04 2012, based on a posting to the Sequence Fans Mailing List by Eric Angelini
%E A215027 Initial term a(0)=0 added by _M. F. Hasler_, Aug 23 2012