A098731 Numbers k such that 2*R_k is a happy number (A007770), where R_k = 11...1 is the repunit (A002275) of length k.

7, 8, 11, 17, 25, 44, 47, 48, 52, 59, 70, 80, 89, 92, 94, 98, 101, 110, 116, 124, 134, 139, 152, 158, 161, 164, 170, 175, 179, 184, 187, 196, 205, 209, 215, 222, 226, 228, 233, 235, 241, 250, 269, 272, 273, 278, 282, 287, 288, 296, 297, 303, 322, 325, 333, 361

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

2*R_11 = 2*11111111111 = 22222222222 is a happy number, so 11 is in the list.

Prog

(Python)
from itertools import count, islice
def A098731_gen(startvalue=1): # generator of terms
    for n in count(max(startvalue, 1)):
        m = n<<2
        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
A098731_list = list(islice(A098731_gen(), 20)) # Chai Wah Wu, Aug 02 2023

Crossrefs

Cf. A007770, A002275.

Sequence in context: A102963 A117619 A226977 * A348784 A294483 A105740

Adjacent sequences: A098728 A098729 A098730 * A098732 A098733 A098734

Keyword

easy,nonn,base

Author

Lambert Klasen (lambert.klasen(AT)gmx.de), Oct 28 2004

Status

approved