A290205 Group identifier of iterated Scrabble function.

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 4, 12, 12, 12, 4, 4, 12, 4, 12, 12, 4, 12, 12, 12, 4, 4, 4, 4, 12, 4, 12, 4, 4, 4, 12, 4, 4, 12, 12, 12, 4, 4, 4, 12, 12, 12, 4, 12, 4, 12, 12, 12, 12, 12, 4, 4, 4, 4, 4

Offset: 0

Author

Michael Turniansky, Jul 24 2017

Keywords

• nonn
• word

Comments

Take the sequence A113172. Map it onto itself repeatedly. You will either end up at the fixed point, 12, or a loop of 4->7->8->9->4 (here represented by 4).

Examples

			For example 10, spelled TEN is worth 3 points, THREE is worth 8 points and 8 is in the 4/7/8/9 loop, so a(10)=4
		

Links

• Wikipedia, Scrabble

Crossrefs

Cf. A113172.

Programs

Python

from num2words import num2words
def A290205(n):
    f = lambda n:sum((1,3,3,2,1,4,2,4,1,8,5,1,3,1,1,3,10,1,1,1,1,4,4,8,4,10)[a] for d in num2words(n).replace(' and ','') if 0<=(a:=ord(d)-97)<=25)
    while True:
        n = f(n)
        if n in {4,7,8,9,4}: return 4
        if n == 12: return 12 # Chai Wah Wu, Apr 21 2023