A325911 - OEIS

%I #39 Apr 02 2023 16:36:51

%S 10,170,2730,43690,699050,11184810,178956970,2863311530,45812984490,

%T 733007751850,11728124029610,187649984473770,3002399751580330,

%U 48038396025285290,768614336404564650,12297829382473034410,196765270119568550570,3148244321913096809130

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

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

%H Colin Barker, <a href="/A325911/b325911.txt">Table of n, a(n) for n = 1..800</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).

%F a(n) = Sum_{i=0..n} 10*16^(i).

%F a(n) = A131865(n-1)*10.

%F a(n) = 10*(16^n-1)/15. - _Andrew Howroyd_, Sep 08 2019

%F From _Colin Barker_, Sep 16 2019: (Start)

%F G.f.: 10*x / ((1 - x)*(1 - 16*x)).

%F a(n) = 17*a(n-1) - 16*a(n-2) for n>2.

%F (End)

%F E.g.f.: (2/3)*exp(x)*(-1 + exp(15*x)). - _Stefano Spezia_, Sep 17 2019

%e a(10) = 733007751850_10 = AAAAAAAAAA_16.

%t 10Accumulate[16^Range[0, 31]] (* _Alonso del Arte_, Sep 17 2019 *)

%t LinearRecurrence[{17,-16},{10,170},20] (* _Harvey P. Dale_, Apr 02 2023 *)

%o (Python)

%o a = 10

%o while a:

%o     a = a*16+10

%o     print(a)

%o (Python)

%o def a(n): return int("A"*n, 16)

%o print([a(n) for n in range(1, 19)]) # _Michael S. Branicky_, Jan 17 2022

%o (PARI) a(n)={10*(16^n-1)/15} \\ _Andrew Howroyd_, Sep 08 2019

%o (PARI) Vec(10*x / ((1 - x)*(1 - 16*x)) + O(x^20)) \\ _Colin Barker_, Sep 16 2019

%Y Cf. A131865, A001025, A228774.

%K nonn,base,easy,dumb

%O 1,1

%A _Eliora Ben-Gurion_, Sep 08 2019