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A003052 Self or Colombian numbers (not of form n + sum of digits of n).
(Formerly M2404)
33
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)
OFFSET

1,2

COMMENTS

Complement of A176995.

A230093(a(n)) = 0. - Reinhard Zumkeller, Oct 11 2013

REFERENCES

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 self-numbers. Volume dedicated to the memory of V. Ramaswami Aiyar. Math. Student 39 (1971), 327--328 (1972). MR0330032 (48 #8371)

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.

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 79--84 (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.

B. Recamán, Problem E2408, Amer. Math. Monthly, 81 (1974), p. 407.

Richard Schorn, Kaprekar's Sequence and his "Selfnumbers", DERIVE Newsletter, #53 (2004), pp. 30-32.

W. Schneider, Self Numbers

T. Trotter, Charlene Numbers

Eric Weisstein's World of Mathematics, Self Number

Wikipedia, Self number

U. Zannier, On the distribution of self-numbers, Proc. Amer. Math. Soc. 85 (1982), 10-14.

Index entries for Colombian or self numbers and related sequences

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(n-1)+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) 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 = filter ((== 0) . a230093) [1..]

-- Reinhard Zumkeller, Oct 11 2013, Aug 21 2011

CROSSREFS

Cf. A006886, A232229.

For self primes, i.e., self numbers which are primes, see A006378.

Cf. A062028, A055642.

See A010061 for the binary version.

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

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Last modified August 29 14:12 EDT 2014. Contains 246192 sequences.