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

%I A090425 #29 Feb 16 2025 08:32:51
%S A090425 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,
%T A090425 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,
%U A090425 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
%N A090425 Number of iterations required for happy number A007770(n) to converge to 1.
%C A090425 The count includes both the start and end.
%H A090425 Reinhard Zumkeller, <a href="/A090425/b090425.txt">Table of n, a(n) for n = 1..10000</a>
%H A090425 T. Cai and Xia Zhou, <a href="http://dx.doi.org/10.1216/RMJ-2008-38-6-1921">On the heights of happy numbers</a>, Rocky Mount. J. Math. 38 (6) (2008) 1921-1926. [From _R. J. Mathar_, Apr 22 2010]
%H A090425 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HappyNumber.html">Happy Number</a>.
%e A090425 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.
%t A090425 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 *)
%o A090425 (Haskell)
%o A090425 a090425 n = snd $ until ((== 1) . fst)
%o A090425                         (\(u, v) -> (a003132 u, v + 1)) (a007770 n, 1)
%o A090425 -- _Reinhard Zumkeller_, Aug 07 2012
%o A090425 (Python)
%o A090425 from itertools import count, islice
%o A090425 def A090425_gen(): # generator of terms
%o A090425     for n in count(1):
%o A090425         c = 1
%o A090425         while n not in {1,37,58,89,145,42,20,4,16}:
%o A090425             n = sum((0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[ord(d)-48] for d in str(n))
%o A090425             c += 1
%o A090425         if n == 1:
%o A090425             yield c
%o A090425 A090425_list = list(islice(A090425_gen(),20)) # _Chai Wah Wu_, Aug 02 2023
%Y A090425 Cf. A007770.
%Y A090425 Cf. A003132.
%K A090425 nonn,base
%O A090425 1,2
%A A090425 _Eric W. Weisstein_, Nov 30 2003