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Search: id:A007770
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| A007770 |
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Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map includes 1. |
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+0
39
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| 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sometimes called friendly numbers, but this usage is deprecated.
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, Sect. E34.
E. El-Sedy and S. Siksek, On happy numbers, Rocky Mountain J. Math. 30 (2000), 565-570.
J. N. Kapur, Reflections of a Mathematician, Chap. 34 pp. 319-324, Arya Book Depot New Delhi 1996.
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LINKS
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Jud McCranie, Table of n, a(n) for n = 1..143071
Hao Pan, Consecutive happy numbers
W. Schneider, Happy Numbers (Includes list of terms below 10000)
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Happy number
Doctor Who, Episode 42
Wikipedia, Doctor Who, Episode 42
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EXAMPLE
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1 is OK. 2 --> 4 --> 16 --> 37 --> ... --> 4, which repeats with period 8, so never reaches 1, so 2 (and 4) are unhappy.
Someone suggested that 98 is happy, but it is not.
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CROSSREFS
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Cf. A001273, A035497 (happy primes), A046519, A031177, A002025, A050972, A050973, A074902.
Cf. A035502, A068571, A072494.
Sequence in context: A096678 A026319 A120153 this_sequence A114961 A123834 A064629
Adjacent sequences: A007767 A007768 A007769 this_sequence A007771 A007772 A007773
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), A.R.McKenzie(AT)bnr.co.uk
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EXTENSIONS
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Doctor Who links from David Applegate, Oct 06 2008
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