OFFSET
1,3
COMMENTS
This sequence has density 1, since all numbers except a thin fraction have digits 0 through 18 in base 100. In particular, there are at most x^0.99782 non-members up to x for large enough x. (This can be improved.) - Charles R Greathouse IV, Jan 30 2014
1263907548 is the smallest term that contains all ten digits. - M. F. Hasler, Jan 30 2014
Where does this first differ from A032945? - R. J. Mathar, Feb 03 2014
This first differs from A032945 at a(110)=910 (followed by 1000, 1001, 1002, ...) while A032945(110)=1000 (followed by 1010, 1020, 1030, ...). - M. F. Hasler, Dec 28 2014
LINKS
T. D. Noe, Table of n, a(n) for n = 1..8495 (terms < 10^6)
FORMULA
a(n) ~ n. - Charles R Greathouse IV, Jan 30 2014
EXAMPLE
Examples of numbers in the sequence:
80 --> 8+0=8
107 --> 1+0=1 / 0+7=7
910 --> 9+1=10 / 1+0=1
1037 --> 1+0=1 / 0+3=3 / 3+7=10
1459 --> 1+4=5 / 4+5=9 / 5+9=14
41358 --> 4+1=5 / 1+3=4 / 3+5=8 / 5+8=13
MATHEMATICA
fQ[n_] := Module[{d, p, s}, d = IntegerDigits[n]; p = Partition[d, 2, 1]; s = Plus @@@ p; Complement[s, Union[d, FromDigits /@ p]] == {}]; Join[Range[0, 9], Select[Range[10, 1000], fQ]] (* T. D. Noe, Jan 30 2014 *)
PROG
(PARI) is(n)=my(d=digits(n), S=Set(d), v=List(), t); for(i=2, #d, listput(v, 10*d[i-1]+d[i])); S=Set(concat(S, Vec(v))); for(i=2, #d, t=d[i-1]+d[i]; if(!setsearch(S, t), return(0))); 1 \\ Charles R Greathouse IV, Jan 13 2015
(Python)
def ok(n):
s = str(n)
return all(str(sum(map(int, s[i:i+2]))) in s for i in range(len(s)-1))
print(list(filter(ok, range(408)))) # Michael S. Branicky, Jun 11 2021
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Eric Angelini, Jan 30 2014
STATUS
approved