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A003052
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Self or Colombian numbers (not of form n + sum of digits of n).
(Formerly M2404)
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23
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1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310, 312, 323, 334, 345, 356, 367, 378, 389, 400, 411, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 514, 525
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Complement of A176995.
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REFERENCES
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M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 116.
D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.
D. R. Kaprekar, The Mathematics of the New Self Numbers (Part V). 311 Devlali Camp, Devlali, India, 1967.
B. Recaman, Problem E2408, Amer. Math. Monthly, 81 (1974), p. 407.
J. Recreational Math., vol. 23, no. 1, p. 244, 1991.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Ulam Spiral of the first 5000 self numbers.
W. Schneider, Self Numbers
T. Trotter, Charlene Numbers
Eric Weisstein's World of Mathematics, Self Number
Wikipedia, Self number
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MAPLE
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isA003052 := proc(n) local k ; for k from 0 to n do if k+A007953(k) = n then RETURN(false): fi; od: RETURN(true) ; end:
A003052 := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do if isA003052(a) then RETURN(a) ; fi; od; fi; end: # R. J. Mathar, Jul 27 2009
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MATHEMATICA
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nn = 525; Complement[Range[nn], Union[Table[n + Total[IntegerDigits[n]], {n, nn}]]] (* T. D. Noe, Mar 31 2013 *)
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PROG
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(PARI) isA003052(n)={ forstep( k=n-1, max(n\2, n-9*#Str(n)), -1, k+A007953(k) == n & return); n } \\ M. F. Hasler, Mar 20 2011
(Haskell)
a003052 n = a003052_list !! (n-1)
a003052_list = f 1 [] where
f n nonSelf | n `elem` nonSelf = f (n+1) nonSelf'
| otherwise = n : f (n+1) nonSelf'
where nonSelf' = take (9 * a055642 n) (a062028 n : nonSelf)
-- Reinhard Zumkeller, Aug 21 2011
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CROSSREFS
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Cf. A006378, A006886.
For self primes, i.e. self numbers which are primes, see A006378.
Cf. A062028, A055642.
Sequence in context: A114136 A025072 A083107 * A003219 A030142 A179085
Adjacent sequences: A003049 A003050 A003051 * A003053 A003054 A003055
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from James A. Sellers, Jul 06 2000
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STATUS
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approved
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