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

%I A325911 #40 Feb 16 2025 08:33:58
%S A325911 10,170,2730,43690,699050,11184810,178956970,2863311530,45812984490,
%T A325911 733007751850,11728124029610,187649984473770,3002399751580330,
%U A325911 48038396025285290,768614336404564650,12297829382473034410,196765270119568550570,3148244321913096809130
%N A325911 Screaming numbers in base 16: numbers whose hexadecimal representation is AAAAAAA...
%C A325911 In any base b > 10, we may express ten as a digit by using the letter A.
%H A325911 Colin Barker, <a href="/A325911/b325911.txt">Table of n, a(n) for n = 1..800</a>
%H A325911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>
%H A325911 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F A325911 a(n) = Sum_{i=0..n} 10*16^(i).
%F A325911 a(n) = A131865(n-1)*10.
%F A325911 a(n) = 10*(16^n-1)/15. - _Andrew Howroyd_, Sep 08 2019
%F A325911 From _Colin Barker_, Sep 16 2019: (Start)
%F A325911 G.f.: 10*x / ((1 - x)*(1 - 16*x)).
%F A325911 a(n) = 17*a(n-1) - 16*a(n-2) for n>2.
%F A325911 (End)
%F A325911 E.g.f.: (2/3)*exp(x)*(-1 + exp(15*x)). - _Stefano Spezia_, Sep 17 2019
%e A325911 a(10) = 733007751850_10 = AAAAAAAAAA_16.
%t A325911 10Accumulate[16^Range[0, 31]] (* _Alonso del Arte_, Sep 17 2019 *)
%t A325911 LinearRecurrence[{17,-16},{10,170},20] (* _Harvey P. Dale_, Apr 02 2023 *)
%o A325911 (Python)
%o A325911 a = 10
%o A325911 while a:
%o A325911     a = a*16+10
%o A325911     print(a)
%o A325911 (Python)
%o A325911 def a(n): return int("A"*n, 16)
%o A325911 print([a(n) for n in range(1, 19)]) # _Michael S. Branicky_, Jan 17 2022
%o A325911 (PARI) a(n)={10*(16^n-1)/15} \\ _Andrew Howroyd_, Sep 08 2019
%o A325911 (PARI) Vec(10*x / ((1 - x)*(1 - 16*x)) + O(x^20)) \\ _Colin Barker_, Sep 16 2019
%Y A325911 Cf. A131865, A001025, A228774.
%K A325911 nonn,base,easy,dumb
%O A325911 1,1
%A A325911 _Eliora Ben-Gurion_, Sep 08 2019