A232087 Second-order base-10 grafting integers.

0, 1, 8, 77, 98, 99, 100, 764, 765, 5711, 5736, 9797, 9998, 9999, 10000, 76394, 77327, 997997, 999998, 999999, 1000000, 2798254, 7639321, 8053139, 25225733, 42808341, 57359313, 60755907, 62996069, 99979997, 99999998, 99999999, 100000000, 127016654

Offset: 1

Author

Robert Tanniru, Nov 17 2013

Keywords

• nonn
• base

Comments

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).

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

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

Examples

			sqrt(764) = 27.64054992...
sqrt(77327) = 278.0773273749...
sqrt(1000000) = 1000.000...
		

References

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

Links

• Robert Tanniru, Introduction to Grafting Numbers.
• Robert Tanniru, PARI code.
• Robert Tanniru, A short note introducing Grafting Numbers and their connection to Catalan Numbers, ResearchGate, 2015.

Crossrefs

Cf. A074841 (subsequence).

Programs

PARI

/* Uses PARI functions provided in link
* Sample run uses a = [0,11], b=10, p=2, direct=FALSE */
GetAllGIs(0,11,10,2,0)