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Search: id:A006753
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| A006753 |
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Smith (or joke) numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity).
(Formerly M3582)
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+0
43
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| 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Of course primes also have this property, trivially.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Gardner, Penrose Tiles to Trapdoor Ciphers. Freeman, NY, 1989, p. 300.
R. K. Guy, Unsolved Problems in the Theory of Numbers, Section B49.
Oltikar, Sham and Keith Wayland. "Construction of Smith Numbers," Mathematics Magazine, vol. 56(1), 1983, pp. 36-37.
C. A. Pickover, "A Brief History of Smith Numbers" in "Wonders of Numbers: Adventures in Mathematics, Mind and Meaning", pp. 247-248, Oxford University Press, 2000.
J. E. Roberts, Lure of the Integers, pp. 269-270 MAA 1992.
D. D. Spencer, Key Dates in Number Theory History, pp. 94. Camelot Pub. Co. FL, 1995.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 180.
A. Wilansky, Smith numbers, Two-Year Coll. Math. J., 13 (1982), 21.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
K. S. Brown's Mathpages, Smith Numbers and Rhonda Numbers
C. K. Caldwell, The Prime Glossary, Smith number
P. J. Costello, Smith Numbers
S. S. Gupta, Smith Numbers
Madras Math's Amazing Number Facts, Smith Numbers
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
C. Riveras, PrimePuzzles.Net, Problem 107:Consecutive Smith numbers
C. Riveras, PrimePuzzles.Net, Problem 108:Methods for generating Smith numbers
W. Schneider, Smith Numbers
Jason T., Smith number
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Smith number
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EXAMPLE
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58=2*29, 58->13, 2->2, 29->11 and indeed 13=2+11.
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CROSSREFS
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Cf. A019506.
Cf. A050224, A050255, A098834-A098840, A103123-A103126, A104166-A104171, A104390, A104391.
Sequence in context: A009925 A059653 A022385 this_sequence A098836 A036920 A036921
Adjacent sequences: A006750 A006751 A006752 this_sequence A006754 A006755 A006756
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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).
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