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A068571
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Number of happy numbers <= 10^n.
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5
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1, 3, 20, 143, 1442, 14377, 143071, 1418854, 14255667, 145674808, 1492609148, 15091199357, 149121303586, 1443278000870, 13770853279685, 130660965862333, 1245219117260664, 12024696404768025, 118226055080025491, 1183229962059381238, 12005034444292997294
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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L. Klasen and Bryan Wolf, Table of n, a(n) for n = 0..1000 (first 122 terms from L. Klasen)
Justin Gilmer, On the density of happy numbers (2011)
L. Klasen, Xeen3d's happy.html
W. Schneider, Happy Numbers
Eric Weisstein's World of Mathematics, Happy Number
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FORMULA
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Contribution from Bryan Wolf, Nov 06 2012: (Begin)
h(n,x) = h(n-1,x-0^2) + h(n-1,x-1^2) + ... + h(n-1,x-9^2) where h() is the number of numbers of length n whose sum of the squares of their digits is x.
a(n) is the sum of all h(n, 0 < x <= 81*n), where x is a happy number, plus 1 for 10^n. (end)
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EXAMPLE
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For n=0, h(0,0) = 1 and h(0,x >0) = 0.
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CROSSREFS
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Cf. A007770, A124095, A219667.
Sequence in context: A082143 A009156 A074573 * A074569 A026303 A154627
Adjacent sequences: A068568 A068569 A068570 * A068572 A068573 A068574
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KEYWORD
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nonn,base
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AUTHOR
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Sascha Kurz, Mar 26 2002
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EXTENSIONS
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More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.de), Nov 03 2004
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STATUS
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approved
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