OFFSET
1,1
COMMENTS
By the definition, k*(k+3) = k*10^m+k. So k+3 = 10^m+1, that is k = 10^m-2. - Seiichi Manyama, Aug 31 2019
LINKS
Index entries for linear recurrences with constant coefficients, signature (11, -10).
FORMULA
a(n) = A002283(n) - 1 = 10^n - 2. - Seiichi Manyama, Aug 31 2019
From Chai Wah Wu, Jun 15 2020: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2.
G.f.: x*(10*x + 8)/((x - 1)*(10*x - 1)). (End)
EXAMPLE
99998*(99998+3) = 9999899998 (concatenation of 99998 and 99998).
PROG
(PARI) for(k=1, 1e9, if(k*(k+3)==eval(Str(k, k)), print1(k", "))) \\ Seiichi Manyama, Aug 31 2019
(PARI) {a(n) = 10^n-2} \\ Seiichi Manyama, Aug 31 2019
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
John W. Layman, Sep 30 2004
EXTENSIONS
a(9)-a(20) from Seiichi Manyama, Aug 31 2019
STATUS
approved