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A236402 Numbers with property that the sum of any pair of adjacent digits is a substring of the number. 6
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)
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 in 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

MAPLE

with(numtheory): P:=proc(n) local a, k, ok; ok:=1; a:=convert(n, base, 10);

for k from 1 to ilog10(n) do if searchtext(convert(a[k]+a[k+1], string), convert(n, string))=0

then ok:=0; break; fi; od; if ok=1 then n; fi; end:

seq(P(i), i=0..10^3); # Paolo P. Lava, Sep 05 2018

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

CROSSREFS

Cf. A236403 (complement).

Cf. A198298, A203565, A203566, A203569.

Sequence in context: A212499 A244890 A032945 * A052018 A302768 A202272

Adjacent sequences:  A236399 A236400 A236401 * A236403 A236404 A236405

KEYWORD

nonn,base,easy

AUTHOR

Eric Angelini, Jan 30 2014

STATUS

approved

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Last modified April 26 11:46 EDT 2019. Contains 322472 sequences. (Running on oeis4.)