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

0, 1, 11, 12, 22, 23, 33, 34, 44, 45, 865, 146, 966, 247, 1067, 348, 1168, 449, 1269, 550, 1370, 651, 1471, 752, 1572, 853, 1673, 954, 1774, 1055, 1875, 1156, 1976, 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

Offset: 0

Author

N. J. A. Sloane, Aug 04 2012, based on a posting to the Sequence Fans Mailing List by Eric Angelini

Keywords

• nonn
• base

Comments

Eric Angelini defined this by saying that "a(n)+a(n+1) = concatenation of n and (n+1)".

An easy induction argument shows that a(n) is always positive.

Examples

			a(100) = concat(99,100) - a(99) = 99 100 - 4590 = 94510.
		

Crossrefs

Cf. A001704, A215028.

Programs

Maple

f:=proc(i) i*10^(1+floor(evalf(log10(i+1), 10)))+i+1; end: # A001704
a:=proc(n) option remember; global f; if n=1 then 1 else f(n-1)-a(n-1); fi; end;

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

Formula

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

Extensions

Initial term a(0)=0 added by M. F. Hasler, Aug 23 2012