login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161874 Bases with smallest unhappy number (in that base) > 2. 3
16, 18, 20, 30, 130, 256, 1042, 4710, 7202, 10082, 47274, 65536, 65600, 351634, 426530, 431730, 764930, 5921514, 26639560, 32435910, 88605010, 97025190, 99562110 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(12) > 50000, if it exists. - Amiram Eldar, Jun 16 2020
a(18) > 1.5*10^6, if it exists. The smallest unhappy numbers corresponding to bases a(1)-a(17) are 3, 7, 3, 5, 20, 3, 12, 3, 3, 14, 3, 3, 3, 3, 3, 3, 23. - Giovanni Resta, Jun 25 2020
The smallest unhappy numbers in bases (a(18), ..., a(23)) are (3, 23, 3, 261, 6, 12). - Lucas A. Brown, Apr 25 2023
a(24) > 10^8, if it exists. - Lucas A. Brown, Apr 25 2023
LINKS
Lucas A. Brown, A161874.c
EXAMPLE
In base 16, 2 is happy because the sequence it generates is 2 -> 4 -> (1,0) -> 1, while 3 is unhappy because the sequence it generates is 3 -> 9 -> (5,1) -> (1,10) -> (6,5) -> (3,13) -> (11,2) -> (7,13) -> (13,10) -> (1,0,13) -> (10,10) -> (12,8) -> (13,0) -> (10,9) -> (11,5) -> (9,2) -> (5,5) -> (3,2) -> (0,13) -> (10,9) -> ..., which repeats with period 6.
MATHEMATICA
happyQ[n_, b_] := NestWhile[Total[IntegerDigits[#, b]^2] &, n, UnsameQ, All] == 1; Select[Range[2, 256], !MemberQ[{2, 4}, #] && happyQ[2, #] &] (* Amiram Eldar, Jun 16 2020 *)
CROSSREFS
Cf. A031177 (unhappy numbers in base 10), A161872, A362026.
Sequence in context: A274127 A328736 A348143 * A095953 A084800 A065426
KEYWORD
nonn,base,more
AUTHOR
Jud McCranie, Jun 20 2009
EXTENSIONS
a(11) from Amiram Eldar, Jun 16 2020
a(12)-a(17) from Giovanni Resta, Jun 25 2020
a(18) from Lucas A. Brown, Aug 17 2022
a(19) from Lucas A. Brown, Aug 26 2022
a(20)-a(23) from Lucas A. Brown, Apr 25 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)