OFFSET
1,2
COMMENTS
The sequence is a permutation of the natural numbers. Sketch of proof: (1) all terms are distinct by definition; (2) each term has a successor (with pandigitals as ultimate candidates); (3) an alleged non-occurring number will succeed the first occurred pandigital number. Cf. A245586. - Reinhard Zumkeller, Jul 26 2014
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
E. Angelini, Add neighbours, use their digits, SeqFan list, Nov. 2, 2013
E. Angelini, Add A to B
E. Angelini, Add A to B [Cached copy, with permission]
EXAMPLE
We see that the result of 1+10 uses only digits from the set {1,1,0} (really a multi-set).
The same with 10+2 which use some elements of {1,0,2}.
Again, 2+19 uses elements of {2,1,9} for its result.
72 is now the smallest integer respecting the constraint (we see that 19+72 is 91 which uses for its transcription only a few elements of {1,9,7,2}).
PROG
(PARI) {subseq(a, b, j)=!for(i=1, #a, while(j<#b, a[i]==b[j++]&&next(2)); return)}
{u=0; a=1; for(n=1, 99, print1(a", "); u+=1<<a; for(t=1, 9e9, bittest(u, t)&&next; subseq(vecsort(digits(a+t)), vecsort(concat(digits(a), digits(t))))||next; a=t; break))}
(Haskell)
import Data.List ((\\), delete)
a228276 n = a228276_list !! (n-1)
a228276_list = 1 : f 1 [2..] where
f x zs = g zs where
g (y:ys) = if null $ show (x + y) \\ (show x ++ show y)
then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Jul 26 2014
CROSSREFS
KEYWORD
AUTHOR
Eric Angelini and M. F. Hasler, Nov 02 2013
EXTENSIONS
Edited by N. J. A. Sloane, Dec 29 2013
STATUS
approved