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Search: id:A113172
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| A113172 |
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Scrabble value of English word for the number n. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (jvospost3(AT)gmail.com), Nov 08 2006
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LINKS
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Landon Curt Noll, The English Name of a Number
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FORMULA
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The standard, non-bonus 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.
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EXAMPLE
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ONE = 1+1+1 = 3, TWO = 1+4+1 = 6, THREE = 1+4+1+1+1 = 8
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MATHEMATICA
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(* 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 *)
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CROSSREFS
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Cf. A080993, A080994.
Sequence in context: A104818 A117540 A010221 this_sequence A128154 A107806 A138965
Adjacent sequences: A113169 A113170 A113171 this_sequence A113173 A113174 A113175
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KEYWORD
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easy,nonn,word
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AUTHOR
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Jack Lloyd (foldalonglines(AT)gmail.com), Jan 07 2006
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EXTENSIONS
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More terms from Robert G. Wilson v Nov 02 2006
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