login
A090425
Number of iterations required for happy number A007770(n) to converge to 1.
4
1, 6, 2, 3, 5, 4, 4, 3, 4, 5, 5, 3, 6, 4, 4, 3, 5, 5, 4, 2, 3, 5, 4, 3, 6, 6, 4, 4, 5, 5, 4, 6, 4, 4, 4, 6, 4, 6, 6, 6, 6, 4, 4, 6, 3, 4, 3, 6, 6, 4, 6, 6, 6, 5, 7, 6, 7, 6, 6, 6, 7, 5, 6, 6, 6, 7, 5, 5, 5, 4, 4, 7, 5, 5, 5, 7, 7, 4, 7, 4, 5, 3, 4, 6, 6, 6, 7, 6, 6, 4, 7, 7, 4, 5, 5, 4, 6, 3, 6, 7, 6, 4
OFFSET
1,2
COMMENTS
The count includes both the start and end.
LINKS
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
A090425_list = list(islice(A090425_gen(), 20)) # Chai Wah Wu, Aug 02 2023
CROSSREFS
Cf. A007770.
Cf. A003132.
Sequence in context: A134105 A167509 A011362 * A160081 A240937 A178054
KEYWORD
nonn,base
AUTHOR
Eric W. Weisstein, Nov 30 2003
STATUS
approved