A232229 a(1)=9; thereafter a(n) = 8*10^(n-1) + 8 + a(n-1).

9, 97, 905, 8913, 88921, 888929, 8888937, 88888945, 888888953, 8888888961, 88888888969, 888888888977, 8888888888985, 88888888888993, 888888888889001, 8888888888889009, 88888888888889017, 888888888888889025, 8888888888888889033, 88888888888888889041, 888888888888888889049, 8888888888888888889057

Offset: 1

Author

N. J. A. Sloane, Nov 22 2013

Keywords

• nonn
• easy

Comments

An infinite subsequence of A003052.

Links

• D. W. Bange, Solution to Problem E 2408, Amer. Math. Monthly, 81 (1974), 407.
• Shyam Sunder Gupta, On Some Marvellous Numbers of Kaprekar, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, 275-315.
• Index entries for Colombian or self numbers and related sequences
• Index entries for linear recurrences with constant coefficients, signature (12,-21,10)

Crossrefs

Cf. A003052, A010061.

Programs

Maple

f:=proc(n) option remember; if n=1 then 9 else
8*10^(n-1)+8+f(n-1); fi; end;
[seq(f(n),n=1..40)];

Mathematica

RecurrenceTable[{a[1]==9,a[n]==8*10^(n-1)+8+a[n-1]},a,{n,30}] (* Harvey P. Dale, May 19 2018 *)

Formula

G.f.: x*(-9+11*x+70*x^2) / ( (10*x-1)*(x-1)^2 ). a(n) = (8*10^n-71)/9+8*n. - R. J. Mathar, Nov 24 2013

Extensions

Definition corrected by Harvey P. Dale, May 19 2018