

A262353


a(n) = ceiling((3sqrt(5))*10^(2*n+1)).


0



8, 764, 76394, 7639321, 763932023, 76393202251, 7639320225003, 763932022500211, 76393202250021031, 7639320225002103036, 763932022500210303591, 76393202250021030359083, 7639320225002103035908264, 763932022500210303590826332, 76393202250021030359082633127
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OFFSET

0,1


COMMENTS

a(n) is a special family of 2ndorder base10 grafting integers, because every integer generated by ceiling((3sqrt(5))*10^(2*n+1)) is a grafting integer.
A grafting number is a number whose digits, represented in base b, appear before or directly after the decimal point of its rth root. Numbers of the simplest type deal with square roots in the decimal system.
The constant x = 3sqrt(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).


REFERENCES

Matt Parker, Things to make and do in the Fourth Dimension, New York (Ferrar, Strauss and Giroux), 2014, p. 6263.


LINKS

Table of n, a(n) for n=0..14.


FORMULA

a(n) = ceiling((3sqrt(5))*10^(2*n+1)).


EXAMPLE

sqrt(8) = 2.828427...,
sqrt(764) = 27.6405...,
sqrt(76394) = 276.39464...


MAPLE

Digits:=2000: a:=n>ceil((3sqrt(5))*10^(2*n+1)); seq(a(n), n=0..14);


MATHEMATICA

Table[Ceiling[(3  Sqrt@ 5) 10^(2 n + 1)], {n, 14}] (* Michael De Vlieger, Mar 24 2016 *)


PROG

(PARI) a(n) = ceil((3sqrt(5))*10^(2*n+1)); \\ Altug Alkan, Mar 24 2016
(PARI) a(n) = 30*100^n  sqrtint(10^(4*n+2)*5) \\ Charles R Greathouse IV, Jan 20 2017
(Magma) [Ceiling((3Sqrt(5))*10^(2*n+1)):n in [0..14]]; // Marius A. Burtea, Aug 08 2019


CROSSREFS

Subsequence of A232087.
Cf. A187799.
Sequence in context: A181153 A184974 A060183 * A268148 A145415 A260032
Adjacent sequences: A262350 A262351 A262352 * A262354 A262355 A262356


KEYWORD

nonn,base


AUTHOR

Martin Renner, Mar 24 2016


EXTENSIONS

a(0) = 8 prepended by Robert Tanniru, Aug 06 2019


STATUS

approved



