

A003052


Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).
(Formerly M2404)


52



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;
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refs;
listen;
history;
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internal format)



OFFSET

1,2


REFERENCES

Max A. Alekseyev, Donovan Johnson and N. J. A. Sloane, On Kaprekar's Junction Numbers, in preparation, 2017.
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.24.
M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 116.
Joshi, V. S. A note on selfnumbers. Volume dedicated to the memory of V. Ramaswami Aiyar. Math. Student 39 (1971), 327328 (1972). MR0330032 (48 #8371)
D. R. Kaprekar, Puzzles of the SelfNumbers. 311 Devlali Camp, Devlali, India, 1959.
D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.
D. R. Kaprekar, The Mathematics of the New Self Numbers (Part V). 311 Devlali Camp, Devlali, India, 1967.
Makowski, Andrzej. On Kaprekar's "junction numbers''. Math. Student 34 1966 77 (1967). MR0223292 (36 #6340)
Narasinga Rao, A. On a technique for obtaining numbers with a multiplicity of generators. Math. Student 34 1966 7984 (1967). MR0229573 (37 #5147)
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Author?, J. Recreational Math., vol. 23, no. 1, p. 244, 1991.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Ulam Spiral of the first 5000 self numbers.
M. Gardner & N. J. A. Sloane, Correspondence, 197374
D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
B. Recamán, Problem E2408, Amer. Math. Monthly, 81 (1974), p. 407.
Richard Schorn, Kaprekar's Sequence and his "Selfnumbers", DERIVE Newsletter, #53 (2004), pp. 3032.
W. Schneider, Self Numbers
N. J. A. Sloane, Martin Gardner, and D. R. Kaprekar, Correspondence, 1974 [Scanned letters]
T. Trotter, Charlene Numbers [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here.  N. J. A. Sloane, Mar 29 2018]
Eric Weisstein's World of Mathematics, Self Number
Wikipedia, Self number
U. Zannier, On the distribution of selfnumbers, Proc. Amer. Math. Soc. 85 (1982), 1014.
Index entries for Colombian or self numbers and related sequences


FORMULA

A230093(a(n)) = 0.  Reinhard Zumkeller, Oct 11 2013
The above defines this sequence: x is in this sequence iff A230093(x) = 0.  M. F. Hasler, Nov 08 2018


MAPLE

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(n1)+1 do if isA003052(a) then RETURN(a) ; fi; od; fi; end: # R. J. Mathar, Jul 27 2009


MATHEMATICA

nn = 525; Complement[Range[nn], Union[Table[n + Total[IntegerDigits[n]], {n, nn}]]] (* T. D. Noe, Mar 31 2013 *)


PROG

(PARI) is_A003052(n)={for(i=1, min(n\2, 9*#digits(n)), sumdigits(ni)==i && return); n} \\ M. F. Hasler, Mar 20 2011, updated Nov 08 2018
(Haskell)
a003052 n = a003052_list !! (n1)
a003052_list = filter ((== 0) . a230093) [1..]
 Reinhard Zumkeller, Oct 11 2013, Aug 21 2011


CROSSREFS

Cf. A006886, A232229, A062028, A055642, A282711.
For self primes, i.e., self numbers which are primes, see A006378.
Complement of A176995.
See A010061 for the binary version, A283002 for a base100 version.
Cf. A247104 (subsequence of squarefree terms).
Sequence in context: A114136 A025072 A083107 * A003219 A030142 A179085
Adjacent sequences: A003049 A003050 A003051 * A003053 A003054 A003055


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from James A. Sellers, Jul 06 2000


STATUS

approved



