OFFSET
1,2
COMMENTS
The next term a(8) is too large to include.
This sequence is infinite - see Theorem 3.1 of El-Sedy and Siksek.
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]
From Amiram Eldar, Aug 03 2025: (Start)
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).
a(14) = 7888{9:160493827157}1{9:34569}3 and a(15) = 77{9:2222222222222220}3{9:97388}3 (Lyons, 2013). (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10
Esam El-Sedy and Samir Siksek, On happy numbers, Rocky Mountain J. Math. 30 (2000), 565-570.
H. G. Grundman and E. A. Teeple, Sequences of consecutive happy numbers, Rocky Mountain J. Math. 37 (6) (2007), 1905-1916.
Daniel Lyons, Smallest numbers beginning sequences of 14 and 15 consecutive happy numbers, Involve, A Journal of Mathematics, Vol. 6, No. 4 (2013), pp. 461-466.
Hao Pan, On consecutive happy numbers, J. Numb. Theory 128 (6) (2008), 1646-1654.
Robert Styer, Smallest Examples of Strings of Consecutive Happy Numbers, J. Int. Seq. 13 (2010), Article 10.6.3.
Robert Styer, Strings of Consecutive Happy Numbers, 2012.
CROSSREFS
KEYWORD
base,nonn,hard,changed
AUTHOR
David W. Wilson, Jun 05 2000
EXTENSIONS
Entry corrected by Sergio Pimentel, Dec 10 2005
STATUS
approved