OFFSET
1,1
COMMENTS
In any base b > 10, we may express ten as a digit by using the letter A.
LINKS
Colin Barker, Table of n, a(n) for n = 1..800
Eric Weisstein's World of Mathematics, Hexadecimal
Index entries for linear recurrences with constant coefficients, signature (17,-16).
FORMULA
a(n) = Sum_{i=0..n} 10*16^(i).
a(n) = A131865(n-1)*10.
a(n) = 10*(16^n-1)/15. - Andrew Howroyd, Sep 08 2019
From Colin Barker, Sep 16 2019: (Start)
G.f.: 10*x / ((1 - x)*(1 - 16*x)).
a(n) = 17*a(n-1) - 16*a(n-2) for n>2.
(End)
E.g.f.: (2/3)*exp(x)*(-1 + exp(15*x)). - Stefano Spezia, Sep 17 2019
EXAMPLE
a(10) = 733007751850_10 = AAAAAAAAAA_16.
MATHEMATICA
10Accumulate[16^Range[0, 31]] (* Alonso del Arte, Sep 17 2019 *)
LinearRecurrence[{17, -16}, {10, 170}, 20] (* Harvey P. Dale, Apr 02 2023 *)
PROG
(Python)
a = 10
while a:
a = a*16+10
print(a)
(Python)
def a(n): return int("A"*n, 16)
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jan 17 2022
(PARI) a(n)={10*(16^n-1)/15} \\ Andrew Howroyd, Sep 08 2019
(PARI) Vec(10*x / ((1 - x)*(1 - 16*x)) + O(x^20)) \\ Colin Barker, Sep 16 2019
CROSSREFS
KEYWORD
nonn,base,easy,dumb
AUTHOR
Eliora Ben-Gurion, Sep 08 2019
STATUS
approved