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%I #33 Sep 08 2022 08:46:14
%S 8,764,76394,7639321,763932023,76393202251,7639320225003,
%T 763932022500211,76393202250021031,7639320225002103036,
%U 763932022500210303591,76393202250021030359083,7639320225002103035908264,763932022500210303590826332,76393202250021030359082633127
%N a(n) = ceiling((3-sqrt(5))*10^(2*n+1)).
%C a(n) is a special family of 2nd-order base-10 grafting integers, because every integer generated by ceiling((3-sqrt(5))*10^(2*n+1)) is a grafting integer.
%C A grafting number is a number whose digits, represented in base b, appear before or directly after the decimal point of its r-th root. Numbers of the simplest type deal with square roots in the decimal system.
%C The constant x = 3-sqrt(5) is a solution of the general grafting equation (x*b^a)^(1/r) = x + c with corresponding values r = 2, b = 10, a = 1, c = 2 (where r >= 2 is the grafting root, b >= 2 is the base in which the numbers are represented, a >= 0 is the number of places the decimal point is shifted, and c >= 0 is the constant added to the front of the result).
%D Matt Parker, Things to make and do in the Fourth Dimension, New York (Ferrar, Strauss and Giroux), 2014, p. 62-63.
%F a(n) = ceiling((3-sqrt(5))*10^(2*n+1)).
%e sqrt(8) = 2.828427...,
%e sqrt(764) = 27.6405...,
%e sqrt(76394) = 276.39464...
%p Digits:=2000: a:=n->ceil((3-sqrt(5))*10^(2*n+1)); seq(a(n),n=0..14);
%t Table[Ceiling[(3 - Sqrt@ 5) 10^(2 n + 1)], {n, 14}] (* _Michael De Vlieger_, Mar 24 2016 *)
%o (PARI) a(n) = ceil((3-sqrt(5))*10^(2*n+1)); \\ _Altug Alkan_, Mar 24 2016
%o (PARI) a(n) = 30*100^n - sqrtint(10^(4*n+2)*5) \\ _Charles R Greathouse IV_, Jan 20 2017
%o (Magma) [Ceiling((3-Sqrt(5))*10^(2*n+1)):n in [0..14]]; // _Marius A. Burtea_, Aug 08 2019
%Y Subsequence of A232087.
%Y Cf. A187799.
%K nonn,base
%O 0,1
%A _Martin Renner_, Mar 24 2016
%E a(0) = 8 prepended by _Robert Tanniru_, Aug 06 2019
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