A113172 -id:A113172 - cp's OEIS frontend

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

Michael Turniansky, Jul 24 2017

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).

			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

Wikipedia, Scrabble

Cf. A113172.

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

A167052 Scrabble value of the Spanish word for the number n.

Original entry on oeis.org

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

Offset: 0

Claudio Meller, Oct 27 2009

The values of letters (in the Spanish version) are: A = 1, B = 3, C = 3, D = 2, E = 1, F = 4, G = 2, H = 4, I = 1, J = 8, K (CH) = 5, L = 1, LL=8, M = 3, N = 1, nasal-N = 8, O = 1, P = 3, Q = 5, R = 1, RR=8, S = 1, T = 1, U = 1, V = 4, X = 8, Y = 4, Z = 10.

(The assignment Q=5 may be incorrect. See the Wikipedia entry. - R. J. Mathar, Nov 03 2009)

			CERO=3+1+1+1=6, UNO=1+1+1=3, DOS=2+1+1=4, TRES=1+1+1+1=4.

Wikipedia, Scrabble.

Cf. A113172.

Offset set to zero - R. J. Mathar, Nov 05 2009

A270004 Run-length encoding of iterated Scrabble function.

Original entry on oeis.org

12, 1, 4, 2, 1, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 3, 4, 1, 1, 1, 3, 1, 2, 3, 3, 3, 1, 1, 1, 5, 6, 3, 1, 2, 4, 3, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 5, 2, 1, 1, 3, 2, 7, 1, 4, 1, 4, 1, 4, 1, 1, 1, 1, 1, 3, 1, 2, 1, 4, 2, 1, 1, 4, 1, 1, 8, 2, 2, 3, 3, 2, 2, 3, 1, 3, 3, 2, 1, 1, 2, 2, 2, 3, 1, 2, 3, 7, 1, 1, 5, 3, 1, 1, 6

Offset: 0

Michael Turniansky, Jul 24 2017

Number of identical consecutive integers in A290205.

Michael Turniansky, Table of n, a(n) for n = 0..455
Wikipedia, Scrabble

Cf. A113172, A290205.

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 A113172(n): return sum(map(pts, num2words(n).replace(" and", "")))
def A290205(n):
    while n not in {12, 4, 7, 8, 9}: n = A113172(n)
    return 12 if n == 12 else 4
def aupton(terms):
    alst, prev, k, rl = [], A290205(0), 1, 1
    while len(alst) < terms:
        while A290205(k) == prev: k += 1; rl += 1
        alst.append(rl); rl = 0; prev = 12 if prev == 4 else 4
    return alst
print(aupton(105)) # Michael S. Branicky, Dec 01 2021

A362437 a(n) = n + Scrabble score of n.

Original entry on oeis.org

13, 4, 8, 11, 11, 15, 16, 15, 17, 13, 13, 20, 24, 24, 25, 28, 30, 29, 30, 27, 32, 36, 40, 43, 43, 47, 48, 47, 49, 45, 42, 46, 50, 53, 53, 57, 58, 57, 59, 55, 51, 55, 59, 62, 62, 66, 67, 66, 68, 64, 64, 68, 72, 75, 75, 79, 80, 79, 81, 77, 75, 79, 83, 86, 86, 90, 91, 90, 92, 88, 83, 87, 91

Offset: 0

N. J. A. Sloane, Apr 21 2023

nonn

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 79.

Cf. A113172.

from num2words import num2words
def A362437(n): return 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) # Chai Wah Wu, Apr 21 2023

A123315 Pascrabble triangle, read by rows.

Original entry on oeis.org

1, 3, 3, 8, 10, 8, 9, 12, 12, 9, 4, 15, 19, 15, 4, 7, 15, 19, 19, 15, 7, 8, 18, 19, 21, 19, 18, 8, 9, 22, 20, 11, 11, 20, 22, 9, 4, 15, 17, 15, 18, 15, 17, 15, 4, 7, 15, 18, 18, 20, 20, 18, 18, 15, 7, 8, 18, 20, 22, 21, 11, 21, 22, 20, 18, 8, 9, 22, 21, 17, 19, 18, 18, 19, 17, 21, 22, 9

Offset: 1

Jonathan Vos Post, Nov 08 2006

The apex of the triangle is 1. Any other value is the Scrabble value of English name for the number which is the sum of the numbers above. This is generated the same way as A007318 Pascal's triangle read by rows, except apply A113172 to each sum. The first column of this triangle is 1, 3, 8, 9, 4, 7, 8, 9, 4, 7, 8, 9, 4, 7... = iterations 1, A113172(1), A113172(A113172(1)), A113172(A113172(A113172(1))). The central pascrabble numbers T(2n+1,n) = 1, 10, 19, 21, 18, 11, 22, ...

			Triangle begins:
row.|.values in row
.1..|01
.2..|03.03
.3..|08.10.08
.4..|09.12.12.09
.5..|04.15.19.15.04
.6..|07.15.19.19.15.07
.7..|08.18.19.21.19.18.08
.8..|09.22.20.11.11.20.22.09
.9..|04.15.17.15.18.15.17.15.04
10..|07.15.18.18.20.20.18.18.15.07
11..|08.18.20.22.21.11.21.22.20.18.8
12..|09.22.21.17.19.18.18.19.17.21.22.09

Cf. A007318 Pascal's triangle read by rows, A113172.

T(1,1) = 1; for i > 1, T(i,j) = A113172(T(i-1, j-1)+T(i-1, j)).

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A290205 Group identifier of iterated Scrabble function.

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A167052 Scrabble value of the Spanish word for the number n.

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A270004 Run-length encoding of iterated Scrabble function.

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A362437 a(n) = n + Scrabble score of n.

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A123315 Pascrabble triangle, read by rows.

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