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

1,1

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

Prog

(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

Crossrefs

Complement of happy numbers A007770. Cf. A056527.

Cf. A003132, A103369.

Sequence in context: A066022 A052047 A078831 * A164119 A308017 A184107

Adjacent sequences: A031174 A031175 A031176 * A031178 A031179 A031180

Keyword

nonn,base

Author

Eric W. Weisstein

Status

approved