

A113172


Scrabble value of English word for the number n.


5



13, 3, 6, 8, 7, 10, 10, 8, 9, 4, 3, 9, 12, 11, 11, 13, 14, 12, 12, 8, 12, 15, 18, 20, 19, 22, 22, 20, 21, 16, 12, 15, 18, 20, 19, 22, 22, 20, 21, 16, 11, 14, 17, 19, 18, 21, 21, 19, 20, 15, 14, 17, 20, 22, 21, 24, 24, 22, 23, 18, 15, 18, 21, 23, 22, 25, 25, 23, 24, 19, 13, 16, 19
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OFFSET

0,1


COMMENTS

The name Scrabble is a registered trademark of Hasbro, Inc. in the US and Canada and of J. W. Spear & Sons PLC elsewhere.
Is 12 the unique fixed point of Scrabble value of English word for the number n, where A113172(n) = n? 12 > "TWELVE" > 1+4+1+1+4+1 > 12. For what n are A113172(n) prime? For what n are there cycles of what length for iterations n, A113172(n), A113172(A113172(n)), A113172(A113172(A113172(n))), ...? For what n does A113172(n)  n? These are key questions in general Scrabblomics.  Jonathan Vos Post, Nov 08 2006


LINKS

Table of n, a(n) for n=0..72.
Landon Curt Noll, The English Name of a Number
Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens


FORMULA

The standard, nonbonus scrabble scoring total of the letters comprising English integer words, given that (A080993) A = 1, B = 3, C = 3, D = 2, E = 1, F = 4, G = 2, H = 4, I = 1, J = 8, K = 5, L = 1, M = 3, N = 1, O = 1, P = 3, Q = 10, R = 1, S = 1, T = 1, U = 1, V = 4, W = 4, X = 8, Y = 4, Z = 10.


EXAMPLE

ONE = 1+1+1 = 3, TWO = 1+4+1 = 6, THREE = 1+4+1+1+1 = 8


MATHEMATICA

(* first copy 'TA' from A109382 then *) ScrabbleTransferRule = {a > 1, b > 3, c > 3, d > 2, e > 1, f > 4, g > 2, h > 4, i > 1, j > 8, k > 5, l > 1, m > 3, n > 1, o > 1, p > 3, q > 10, r > 1, s > 1, t > 1, u > 1, v > 4, w > 4, x > 8, y > 4, z > 10}; f[n_] := Plus @@ (Flatten@ Part[TA, n + 1] /. ScrabbleTransferRule); Table[ f@n, {n, 0, 72}] (* Robert G. Wilson v *)


PROG

(Python)
from num2words import num2words
tp = {"aeilnorstu": 1, "dg": 2, "bcmp":3, "fhvwy":4, "k":5, "jx":8, "qz":10}
def pts(c): return ([tp[s] for s in tp if c in s]+[0])[0]
def a(n): return sum(map(pts, num2words(n).replace(" and", "")))
print([a(n) for n in range(73)]) # Michael S. Branicky, Aug 18 2021


CROSSREFS

Cf. A000027, A080993, A080994.
Sequence in context: A280009 A117540 A010221 * A128154 A213538 A264971
Adjacent sequences: A113169 A113170 A113171 * A113173 A113174 A113175


KEYWORD

easy,nonn,word


AUTHOR

Jack Lloyd (foldalonglines(AT)gmail.com), Jan 07 2006


EXTENSIONS

More terms from Robert G. Wilson v, Nov 02 2006


STATUS

approved



