def four_digit_figurate(size):
for n in figurate_numbers(size):
if n < 1000:
continue
if n >= 10000:
break
yield n
def search_pentagonal_sum_difference():
# Find pentagonal numbers a and b such that a + b and a - b are also pentagonal.
# Treat c = a + b as fundamental, and derive b and a - b from it
# b = c - a
# (a - b) = a - (c - a) = 2 * a - c
seen = set()
seen_list = []
for c in figurate_numbers(5):
for a in seen_list:
b = c - a
a_minus_b = 2 * a - c
#assert a_minus_b == a - b
#assert a + b == c
if b in seen and a_minus_b in seen:
return a_minus_b
seen.add(c)
seen_list.append(c)
from utility import up_to, figurate_numbers
def letter_value(c):
"""
>>> [letter_value(c) for c in 'abcdefghijklmnopqrstuvwxyz']
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]
"""
c = c.lower()
return ord(c) - ord('a') + 1
def word_value(word):
"""
>>> word_value('sky')
55
"""
return sum(letter_value(c) for c in word)
with open('data/words.txt') as f:
word_data = f.read()
words = [w.strip('"').lower() for w in word_data.split(',')]
t_nums = set(up_to(30 * 26, figurate_numbers(3)))
print(sum(1 for w in words if word_value(w) in t_nums))
def tri_pent_hex_numbers():
for n in figurate_numbers(6):
if is_triangular_number(n) and is_pentagonal_number(n):
yield n
