A228276 Sum of a(n)+a(n+1) can be written using the digits of {a(n),a(n+1)}; always choose the smallest possible unused positive integer.

1, 10, 2, 19, 72, 100, 3, 20, 4, 30, 5, 40, 6, 50, 7, 60, 8, 70, 9, 12, 79, 18, 13, 68, 113, 198, 21, 91, 32, 181, 130, 170, 131, 82, 120, 80, 101, 89, 109, 23, 69, 27, 14, 28, 54, 17, 24, 58, 117, 124, 90, 11, 200, 15, 36, 26, 37, 126, 93, 41, 273, 52, 163, 29, 63, 107, 123, 96, 71, 230, 73, 241, 83, 152, 64, 182, 31, 92, 119, 78, 102, 99

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]

Index entries for sequences that are permutations of the natural numbers

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

Cf. A234932, A234934, A234935.

Cf. A245586 (inverse).

Sequence in context: A364188 A326107 A005483 * A040099 A330365 A173237

Adjacent sequences: A228273 A228274 A228275 * A228277 A228278 A228279

Keyword

nonn,base,look

Author

Eric Angelini and M. F. Hasler, Nov 02 2013

Extensions

Edited by N. J. A. Sloane, Dec 29 2013

Status

approved