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

1,1

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

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.

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.

Cf. A062028, A007953, A055642, A230093.

Sequence in context: A081472 A097660 A238898 * A225793 A154809 A153170

Adjacent sequences: A176992 A176993 A176994 * A176996 A176997 A176998

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 21 2011

Status

approved