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

1,3

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 members.

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

References

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

Links

Table of n, a(n) for n=1..34.

Robert Tanniru, Introduction to Grafting Numbers

Robert Tanniru, PARI Code

Example

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

Prog

(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)

Crossrefs

Cf. A074841 (subsequence).

Sequence in context: A231286 A251927 A024281 * A105429 A225348 A091686

Adjacent sequences: A232084 A232085 A232086 * A232088 A232089 A232090

Keyword

nonn,base

Author

Robert Tanniru, Nov 17 2013

Status

approved