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A236402
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Numbers with property that the sum of any pair of adjacent digits is a substring of the number.
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7
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 400, 401, 402, 403, 404, 405, 406, 407
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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