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A230094 Numbers n that can be expressed as (m + sum of digits of m) in exactly two ways. 5
101, 103, 105, 107, 109, 111, 113, 115, 117, 202, 204, 206, 208, 210, 212, 214, 216, 218, 303, 305, 307, 309, 311, 313, 315, 317, 319, 404, 406, 408, 410, 412, 414, 416, 418, 420, 505, 507, 509, 511, 513, 515, 517, 519, 521, 606, 608, 610, 612, 614, 616, 618, 620, 622, 707, 709, 711, 713, 715, 717, 719, 721, 723, 808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that A230093(n) = 2.

The sequence "Numbers n such that A230093(n) = 3" starts at 10^13+1 (see A230092). This implies that changing the definition of A230094 to "Numbers n such that A230093(n) >= 2" (the so-called "junction numbers") would produce a sequence which agrees with A230094 up to 10^13.

Makowski shows that the sequence of junction numbers is infinite.

REFERENCES

Max A. Alekseyev, Donovan Johnson and N. J. A. Sloane, On Kaprekar's Junction Numbers, in preparation, 2017.

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, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.

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)

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]

Index entries for Colombian or self numbers and related sequences

EXAMPLE

a(1) = 101 = 91 + (9+1) = 100 + (1+0+0);

a(10) = 202 = 191 + (1+9+1) = 200 + (2+0+0);

a(100) = 1106 = 1093 + (1+0+9+3) = 1102 + (1+1+0+2);

a(1000) = 10312 = 10295 + (1+0+2+9+5) = 10304 + (1+0+3+0+4).

MAPLE

For Maple code see A230093.

PROG

(Haskell)

a230094 n = a230094_list !! (n-1)

a230094_list = filter ((== 2) . a230093) [0..]

-- Reinhard Zumkeller, Oct 11 2013

CROSSREFS

Cf. A007953, A062028, A004207, A230093, A003052, A176995, A225793, A230092, A230093, A227915.

Sequence in context: A271642 A164849 A162671 * A030474 A162199 A195469

Adjacent sequences:  A230091 A230092 A230093 * A230095 A230096 A230097

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Oct 10 2013, Oct 24 2013

STATUS

approved

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Last modified August 21 17:55 EDT 2017. Contains 290893 sequences.