A031177 Unhappy numbers: numbers having period-8 2-digitized sequences.

2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 83

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digitaddition
• Eric Weisstein's World of Mathematics, Unhappy Number

Crossrefs

Complement of happy numbers A007770. Cf. A056527.

Cf. A003132, A103369.

Programs

Haskell

a031177 n = a031177_list !! (n-1)
a031177_list = filter ((/= 1) . a103369) [1..]
-- Reinhard Zumkeller, Aug 24 2011

Python

from itertools import count, islice
def A031177_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        m = n
        while m not in {1,37,58,89,145,42,20,4,16}:
            m = sum((0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[ord(d)-48] for d in str(m))
        if m > 1:
            yield n
A031177_list = list(islice(A031177_gen(),20)) # Chai Wah Wu, Aug 02 2023