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

0,1

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).

Links

Table of n, a(n) for n=0..72.

Wikipedia, Scrabble

Example

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

Prog

(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

Crossrefs

Cf. A113172.

Sequence in context: A273339 A088899 A258199 * A066014 A080678 A096300

Adjacent sequences: A290202 A290203 A290204 * A290206 A290207 A290208

Keyword

nonn,word

Author

Michael Turniansky, Jul 24 2017

Status

approved