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

1,1

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.

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

Table of n, a(n) for n=1..38.

Colin 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.

Example

24 = (2*sqrt(4))!, 36 = 3!*6, 127 = -1 + 2^7.

Crossrefs

Cf. A080035, A119710.

Sequence in context: A281925 A261022 A179152 * A347422 A278474 A327946

Adjacent sequences: A193066 A193067 A193068 * A193070 A193071 A193072

Keyword

base,nonn,more

Author

Colin Rose, Aug 08 2011

Status

approved