login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317330 a(n) is the smallest positive integer not yet in the sequence that contains a digit equal to the sum of the digits of a(n-1) (mod 10); a(1)=0. 2
0, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 20, 21, 23, 25, 27, 29, 31, 24, 26, 28, 30, 32, 35, 38, 41, 45, 39, 22, 34, 37, 40, 42, 36, 49, 33, 46, 50, 51, 56, 61, 47, 71, 48, 52, 57, 62, 58, 43, 67, 53, 68, 44, 78, 54, 59, 64, 60, 63, 69, 55, 70, 72, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Up to n=150 the only consecutive terms in the sequence are 19,20,21; 50,51; 90,91; 100,101; 106,107; 108,109,110.
Up to n=150 the sequence of first differences is bounded by -57 and 57 (in nonconsecutive terms).
From Robert G. Wilson v, Jul 26 2018: (Start)
It appears that every number appears.
If so the inverse permutation would be: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 21, 37, 22, 27, 23, ..., .
(End)
Yes, every number appears. Every pandigital number must eventually appear, and for each d in [0,9] there are infinitely many pandigital numbers with digit sum == d (mod 10), so every number containing digit d will eventually appear. - Robert Israel, Aug 30 2018
LINKS
EXAMPLE
a(5)=2 since a(4)=11 and 1+1 is congruent to 2 (mod 10).
a(21)=20 since a(20)=19 and 1+9 is congruent to 0 (mod 10).
MAPLE
N:= 1000: # to get all terms before the first term > N
A[1]:= 0:
for d from 0 to 9 do S[d]:= select(t -> member(d, convert(t, base, 10)), {$1..N}) od:
for n from 2 do
dd:= convert(convert(A[n-1], base, 10), `+`) mod 10;
if S[dd] = {} then break fi;
A[n]:= min(S[dd]);
for d from 0 to 9 do S[d]:= S[d] minus {A[n]} od:
od:
seq(A[i], i=1..n-1); # Robert Israel, Aug 30 2018
MATHEMATICA
f[lst_List] := Block[{k = 1, l = Mod[Plus @@ IntegerDigits@lst[[-1]], 10]}, While[MemberQ[lst, k] || Union[MemberQ[{l}, #] & /@ IntegerDigits@k][[-1]] == False, k++]; Append[lst, k]]; Nest[f, {0}, 72] (* Robert G. Wilson v, Jul 26 2018 *)
CROSSREFS
Cf. A107353.
Sequence in context: A366360 A182620 A366013 * A238880 A340138 A332177
KEYWORD
nonn,base
AUTHOR
Enrique Navarrete, Jul 25 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)