OFFSET
1,2
COMMENTS
No two consecutive values appear in this sequence (see Links). - Griffin N. Macris, May 31 2020
The asymptotic density of this sequence is (1/8) * (2 - Sum_{n>=1} 1/2^a(n))^2 = 0.252660... (A242403). - Amiram Eldar, Nov 28 2020
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.24, pp. 179-180.
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, pp. 384-386.
G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers, Bolletino U. M. I. (7) 9-A (1995), 143-148.
LINKS
Antti Karttunen, 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 [math.NT], 2021-2022; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.
Griffin N. Macris, Proof that no consecutive self numbers exist, 2020.
G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers. II, Bollettino dell'Unione Matematica Italiana, 2-A (1999), 397-399.
MAPLE
# For Maple code see A230091. - N. J. A. Sloane, Oct 10 2013
MATHEMATICA
Table[n + Total[IntegerDigits[n, 2]], {n, 0, 300}] // Complement[Range[Last[#]], #]& (* Jean-François Alcover, Sep 03 2013 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(Haskell)
a010061 n = a010061_list !! (n-1)
a010061_list = filter ((== 0) . a228085) [1..]
-- Reinhard Zumkeller, Oct 13 2013
(PARI)
/* Gen(n, b) returns a list of the generators of n in base b. Written by Max Alekseyev (see Alekseyev et al., 2021).
For example, Gen(101, 10) returns [91, 101]. - N. J. A. Sloane, Jan 02 2022 */
{ Gen(u, b=10) = my(d, m, k);
if(u<0 || u==1, return([]); );
if(u==0, return([0]); );
d = #digits(u, b)-1;
m = u\b^d;
while( sumdigits(m, b) > u - m*b^d,
m--;
if(m==0, m=b-1; d--; );
);
k = u - m*b^d - sumdigits(m, b);
vecsort( concat( apply(x->x+m*b^d, Gen(k, b)),
apply(x->m*b^d-1-x, Gen((b-1)*d-k-2, b)) ) );
}
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Antti Karttunen, Aug 17 2013
Better definition from Matthew C. Russell, Oct 08 2013
STATUS
approved