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A055629 Beginning of first run of at least n consecutive happy numbers.

%I A055629 #40 Aug 04 2025 02:20:02
%S A055629 1,31,1880,7839,44488,7899999999999959999999996,
%T A055629 7899999999999959999999996
%N A055629 Beginning of first run of at least n consecutive happy numbers.
%C A055629 The next term a(8) is too large to include.
%C A055629 This sequence is infinite - see Theorem 3.1 of El-Sedy and Siksek.
%C A055629 With notation {9:repeat_count_of_digit_nine}, a(8) = 58{9:11}6{9:144}5, a(9) = 26{9:137}7{9:74}5, a(10) = 38{9:560}0{9:87}5. - Lambert Klasen (lambert.klasen(AT)postmaster.co.uk), Oct 17 2004 [a(9)-a(10) were corrected, using Styer's paper, by _Amiram Eldar_, Aug 03 2025]
%C A055629 From _Amiram Eldar_, Aug 03 2025: (Start)
%C A055629 a(11) = 27{9:280}0{9:1287}4, a(12) = 388{9:158021}8{9:136 nines}4, and a(13) = 288{9:218491}3{9:385203}3 (Styer, 2010).
%C A055629 a(14) = 7888{9:160493827157}1{9:34569}3 and a(15) = 77{9:2222222222222220}3{9:97388}3 (Lyons, 2013). (End)
%H A055629 Amiram Eldar, <a href="/A055629/b055629.txt">Table of n, a(n) for n = 1..10</a>
%H A055629 Esam El-Sedy and Samir Siksek, <a href="http://dx.doi.org/10.1216/rmjm/1022009281">On happy numbers</a>, Rocky Mountain J. Math. 30 (2000), 565-570.
%H A055629 H. G. Grundman and E. A. Teeple, <a href="http://dx.doi.org/10.1216/rmjm/1199649829">Sequences of consecutive happy numbers</a>, Rocky Mountain J. Math. 37 (6) (2007), 1905-1916.
%H A055629 Daniel Lyons, <a href="http://dx.doi.org/10.2140/involve.2013.6.461">Smallest numbers beginning sequences of 14 and 15 consecutive happy numbers</a>, Involve, A Journal of Mathematics, Vol. 6, No. 4 (2013), pp. 461-466.
%H A055629 Hao Pan, <a href="http://dx.doi.org/10.1016/j.jnt.2007.11.009">On consecutive happy numbers</a>, J. Numb. Theory 128 (6) (2008), 1646-1654.
%H A055629 Robert Styer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Styer/styer5.html">Smallest Examples of Strings of Consecutive Happy Numbers</a>, J. Int. Seq. 13 (2010), Article 10.6.3.
%H A055629 Robert Styer, <a href="https://homepage.villanova.edu/robert.styer/HappyNumbers/happy_numbers.htm">Strings of Consecutive Happy Numbers</a>, 2012.
%Y A055629 Cf. A007770.
%K A055629 base,nonn,hard
%O A055629 1,2
%A A055629 _David W. Wilson_, Jun 05 2000
%E A055629 Entry corrected by _Sergio Pimentel_, Dec 10 2005