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%I #15 Aug 30 2022 14:29:05
%S 6,3,3,6,4,5,3,1,12,5,19,2,9,3,4,5,3,3,3,3,6,20,1,3,6,28,9,12,2,2,1,
%T 10,5,11,7,4,6,3,23,1,17,11,2,8,1,8,3,6,1,6,3,2,7,18,6,3,2,1,8,3,4,3,
%U 5,1,5,7,5,31,6,18,5,9,9,3,6,40,20,7,2,1,42,9,5,1,9,3,2,1
%N First differences of A007770 (happy numbers).
%C El-Sedy and Siksek show that there exist arbitrarily long runs of consecutive integers that are happy numbers. So this sequence contains arbitrarily long runs of 1's.
%H E. El-Sedy and S. Siksek, <a href="https://doi.org/10.1216/rmjm/1022009281">On happy numbers</a>, Rocky Mountain J. Math. 30 (2000), 565-570.
%F a(n) = A007770(n+1) - A007770(n), where A007770(n) is the n-th happy number.
%t happyQ[n_] := NestWhile[Plus @@ (IntegerDigits[#]^2) &, n, UnsameQ, All] == 1; Differences @ Select[Range[700], happyQ] (* _Amiram Eldar_, Aug 06 2022 *)
%o (Python)
%o from itertools import count, islice
%o def ssd(n): return sum(int(d)**2 for d in str(n))
%o def ok(n):
%o while n not in [1, 4]: n = ssd(n) # iterate until fixed point/cycle
%o return n==1
%o def agen(): # generator of terms
%o prevk = 1
%o for k in count(2):
%o if ok(k): yield k - prevk; prevk = k
%o print(list(islice(agen(), 88))) # _Michael S. Branicky_, Aug 06 2022
%Y Cf. A007770.
%K nonn,base
%O 1,1
%A _Darío D. Devia_, Aug 05 2022
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