A325911 Screaming numbers in base 16: numbers whose hexadecimal representation is AAAAAAA...

10, 170, 2730, 43690, 699050, 11184810, 178956970, 2863311530, 45812984490, 733007751850, 11728124029610, 187649984473770, 3002399751580330, 48038396025285290, 768614336404564650, 12297829382473034410, 196765270119568550570, 3148244321913096809130

Offset: 1

Author

Eliora Ben-Gurion, Sep 08 2019

Keywords

• nonn
• base
• easy
• dumb

Comments

In any base b > 10, we may express ten as a digit by using the letter A.

Examples

			a(10) = 733007751850_10 = AAAAAAAAAA_16.
		

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).

Crossrefs

Cf. A131865, A001025, A228774.

Programs

Mathematica

10Accumulate[16^Range[0, 31]] (* Alonso del Arte, Sep 17 2019 *)
LinearRecurrence[{17,-16},{10,170},20] (* Harvey P. Dale, Apr 02 2023 *)

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

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

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