A193069 Pretty wild narcissistic numbers - numbers that pwn: - an integer n that can be expressed using just the digits of n (each digit used once only and in order from left to right) and the operators + - * / ^ ! and the radical symbol. Concatenation is allowed.

24, 36, 71, 119, 120, 127, 143, 144, 145, 216, 240, 343, 354, 355, 360, 384, 456, 595, 660, 693, 713, 715, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 733, 736, 744, 799, 936

Offset: 1

Author

Colin Rose, Aug 08 2011

Keywords

• base
• nonn

Comments

Unlike 'radical narcissistic numbers', the pretty wild variety are allowed to use factorials.

Pretty wild narcissistic numbers nest both radical narcissistic numbers and ordered (nice) Friedman numbers.

Examples

			24 = (2 Sqrt[4])! , 36 = 3! 6,  127 = -1 + 2^7
		

References

• J. S. Madachy, Mathematics on Vacation, Thomas Nelson and Sons, (1966), pp. 163 - 175.
• Colin Rose, "Radical Narcissistic numbers", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 250-254.

Links

• C. Rose, Pretty Wild Narcissistic Numbers - numbers that pwn
• Inder J. Taneja, Selfie Numbers-IV: Addition, Subtraction and Factorial, RGMIA Research Report Collection, 19 (2016), #163, pp. 1-42.
• Inder J. Taneja, Selfie Numbers, Fibonacci Sequence and Selfie Fractions, RGMIA Collection, 19 (2016), #167, pp. 1-24.
• Wikipedia, Friedman number

Crossrefs

Cf. A080035, A119710