OFFSET
1,2
COMMENTS
The count includes both the start and end.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
T. Cai and Xia Zhou, On the heights of happy numbers, Rocky Mount. J. Math. 38 (6) (2008) 1921-1926. [From R. J. Mathar, Apr 22 2010]
Eric Weisstein's World of Mathematics, Happy Number.
EXAMPLE
7 is the 2nd happy number and iterated digit squarings and additions give the sequence {7,49,97,130,10,1}, so a(2)=6.
MATHEMATICA
happy[n_] := If[(list = NestWhileList[Plus @@ (IntegerDigits[#]^2) &, n, UnsameQ, All])[[-1]] == 1, Length[list] - 1, Nothing]; Array[happy, 700] (* Amiram Eldar, Apr 12 2022 *)
PROG
(Haskell)
a090425 n = snd $ until ((== 1) . fst)
(\(u, v) -> (a003132 u, v + 1)) (a007770 n, 1)
-- Reinhard Zumkeller, Aug 07 2012
(Python)
from itertools import count, islice
def A090425_gen(): # generator of terms
for n in count(1):
c = 1
while n not in {1, 37, 58, 89, 145, 42, 20, 4, 16}:
n = sum((0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[ord(d)-48] for d in str(n))
c += 1
if n == 1:
yield c
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric W. Weisstein, Nov 30 2003
STATUS
approved