A259571 Numbers n whose square root contains at least one instance of n in the first n digits after the decimal point.

3, 7, 8, 17, 23, 27, 38, 39, 43, 48, 58, 65, 66, 67, 68, 69, 74, 75, 76, 77, 78, 83, 84, 88, 89, 91, 92, 93, 98, 99, 105, 110, 113, 140, 156, 157, 170, 182, 186, 188, 191, 194, 205, 212, 215, 218, 222, 227, 229, 234, 235, 241, 246, 247, 252, 267, 287, 293, 294

Offset: 1

Author

Andreas Boe, Jun 30 2015

Keywords

• nonn
• base

Comments

Numbers beginning with a nine are most likely to have this property, and numbers beginning with a one are least likely. No squares have it.

Examples

			sqrt(17) = 4.12310562561766054... The first 17 digits after the decimal point contain "17".
		

Links

• Andreas Boe, Table of n, a(n) for n = 1..551

Programs

Mathematica

Select[Range@ 301, ! StringFreeQ[ToString@ FromDigits@ First@ RealDigits@ N[Sqrt@ #, #], ToString@ #] &] // Rest (* Michael De Vlieger, Jul 02 2015 *)