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 A230094 Numbers that can be expressed as (m + sum of digits of m) in exactly two ways. 6
 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 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 Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory, 2022 (to appear). Santanu Bandyopadhyay, Self-Number, Indian Institute of Technology Bombay (Mumbai, India, 2020). Santanu Bandyopadhyay, Self-Number, Indian Institute of Technology Bombay (Mumbai, India, 2020). [Local copy] David A. Corneth, Examples 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. MATHEMATICA Position[#, 2][[All, 1]] - 1 &@ Sort[Join[#2, Map[{#, 0} &, Complement[Range[#1], #2[[All, 1]]]] ] ][[All, -1]] & @@ {#, Tally@ Array[# + Total@ IntegerDigits@ # &, # + 1, 0]} &[10^3] (* Michael De Vlieger, Oct 28 2020, after Harvey P. Dale at A230093 *) PROG (Haskell) a230094 n = a230094_list !! (n-1) a230094_list = filter ((== 2) . a230093) [0..] -- Reinhard Zumkeller, Oct 11 2013 CROSSREFS Cf. A003052, A007953, A004207, A048528, A062028, A176995, A225793, A227915, A230092, A230093. 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 April 23 09:48 EDT 2024. Contains 371905 sequences. (Running on oeis4.)