A090425 Number of iterations required for happy number A007770(n) to converge to 1.

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

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
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

Adjacent sequences: A090422 A090423 A090424 * A090426 A090427 A090428

Keyword

nonn,base

Author

Eric W. Weisstein, Nov 30 2003

Status

approved