A232087 - OEIS

%I #36 May 23 2024 07:08:24

%S 0,1,8,77,98,99,100,764,765,5711,5736,9797,9998,9999,10000,76394,

%T 77327,997997,999998,999999,1000000,2798254,7639321,8053139,25225733,

%U 42808341,57359313,60755907,62996069,99979997,99999998,99999999,100000000,127016654

%N Second-order base-10 grafting integers.

%C Second-order base-10 grafting integers are integers that, when expressed in base 10, will appear in their own square root before or directly after the decimal point (ignoring leading 0's and including trailing 0's).

%C All numbers of the form 10^2n, 10^2n - 1, and 10^2n - 2, n >= 1, are terms.

%C All numbers of the form (10^n-3)*(10^n+1), n > 0, are terms.

%D Robert Tanniru, A short note introducing Grafting Numbers and their connection to Catalan Numbers, J. Comb. Math. and Comb. Computing, 95 (2015), 309-312.

%H Robert Tanniru, <a href="http://roberttanniru.weebly.com/grafting-numbers.html">Introduction to Grafting Numbers</a>.

%H Robert Tanniru, <a href="/A232087/a232087.txt">PARI code</a>.

%H Robert Tanniru, <a href="https://www.researchgate.net/publication/301633218_A_short_note_introducing_grafting_numbers_and_their_connection_to_Catalan_Numbers">A short note introducing Grafting Numbers and their connection to Catalan Numbers</a>, ResearchGate, 2015.

%e sqrt(764) = 27.64054992...

%e sqrt(77327) = 278.0773273749...

%e sqrt(1000000) = 1000.000...

%o (PARI)

%o /* Uses PARI functions provided in link

%o * Sample run uses a = [0,11], b=10, p=2, direct=FALSE */

%o GetAllGIs(0,11,10,2,0)

%Y Cf. A074841 (subsequence).

%K nonn,base

%O 1,3

%A _Robert Tanniru_, Nov 17 2013