A062118 Numbers k such that k^2 has k as its middle digits.

1, 50, 60, 250, 3792, 7600, 376000, 495475, 625000, 971582, 66952741, 93760000, 177656344, 3199268655, 9062500000, 10937600000, 788138178328, 860628177919, 890625000000, 2291665833333, 2780225311054, 2890625000000, 71093760000000, 128906250000000

Offset: 1

Author

Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), Jun 28 2001

Keywords

• nonn
• base
• nice

Comments

Some of the terms are automorphic numbers (A003226) multiplied by an appropriate power of 10. a(25) > 10^15. - Giovanni Resta, Jul 29 2013

Examples

			a(5)=3792 because 3792^2 = 14379264 has 3792 as its middle digits.
		

References

• Computed by Robert Israel.

Crossrefs

k^2 is given in A062120.

Programs

Mathematica

Do[ If[ StringPosition[ ToString[n^2], ToString[n]] [[1, 1]] == (Ceiling[ Log[10, n^2] ] - Ceiling[ Log[10, n] ])/2 + 1, Print[n] ], {n, 1, 10^9} ]

Extensions

Corrected and extended by Robert G. Wilson v, Aug 08 2001

a(15)-a(24) from Giovanni Resta, Jul 29 2013