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A176995 Numbers that can be written as (m + sum of digits of m) for some m. 22
2, 4, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is approximately 0.9022222 (Guaraldo, 1978). - Amiram Eldar, Nov 22 2020
REFERENCES
V. S. Joshi, A note on self-numbers. Volume dedicated to the memory of V. Ramaswami Aiyar, Math. Student, Vol. 39 (1971), pp. 327-328. MR0330032 (48 #8371).
Andrzej Makowski, On Kaprekar's "junction numbers", Math. Student, Vol. 34 (1966), p. 77. MR0223292 (36 #6340).
A. Narasinga Rao, On a technique for obtaining numbers with a multiplicity of generators, Math. Student, Vol. 34 (1966), pp. 79-84. MR0229573 (37 #5147).
LINKS
Rosalind Guaraldo, On the Density of the Image Sets of Certain Arithmetic Functions - II, The Fibonacci Quarterly, Vol. 16, No. 5 (1978), pp. 481-488.
Eric Weisstein's World of Mathematics, Self Number.
Wikipedia, Self number.
FORMULA
A230093(a(n)) > 0. - Reinhard Zumkeller, Oct 11 2013
EXAMPLE
a(5) = 10 = 5 + (5);
a(87) = 100 = 86 + (8+6);
a(898) = 1000 = 977 + (9+7+7);
a(9017) = 10000 = 9968 + (9+9+6+8).
MATHEMATICA
Select[Union[Table[n + Total[IntegerDigits[n]], {n, 77}]], # <= 77 &] (* Jayanta Basu, Jul 27 2013 *)
PROG
(Haskell)
a176995 n = a176995_list !! (n-1)
a176995_list = filter ((> 0) . a230093) [1..]
-- Reinhard Zumkeller, Oct 11 2013, Aug 21 2011
(PARI) is_A003052(n)={for(i=1, min(n\2, 9*#digits(n)), sumdigits(n-i)==i && return); n} \\ from A003052
isok(n) = ! is_A003052(n) \\ Michel Marcus, Aug 20 2020
CROSSREFS
Complement of A003052, range of A062028.
Sequence in context: A081472 A097660 A238898 * A225793 A154809 A153170
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Aug 21 2011
STATUS
approved

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Last modified July 17 08:16 EDT 2024. Contains 374360 sequences. (Running on oeis4.)