A176995 Numbers that can be written as (m + sum of digits of m) for some m.

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

Offset: 1

Author

Reinhard Zumkeller, Aug 21 2011

Keywords

• nonn
• base

Comments

The asymptotic density of this sequence is approximately 0.9022222 (Guaraldo, 1978). - Amiram Eldar, Nov 22 2020

Examples

			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).
		

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).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• 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.
• Andrzej Makowski, On Kaprekar's "junction numbers", Math. Student, Vol. 34, No. 2 (1966), p. 77. MR0223292 (36 #6340); entire issue.
• A. Narasinga Rao, On a technique for obtaining numbers with a multiplicity of generators, Math. Student, Vol. 34, No. 2 (1966), pp. 79-84. MR0229573 (37 #5147); entire issue.
• Eric Weisstein's World of Mathematics, Self Number.
• Wikipedia, Self number.

Crossrefs

Complement of A003052, range of A062028.

Cf. A062028, A007953, A055642, A230093.

Programs

Haskell

a176995 n = a176995_list !! (n-1)
a176995_list = filter ((> 0) . a230093) [1..]
-- Reinhard Zumkeller, Oct 11 2013, Aug 21 2011

Mathematica

Select[Union[Table[n + Total[IntegerDigits[n]], {n, 77}]], # <= 77 &] (* Jayanta Basu, Jul 27 2013 *)

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

Formula

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