A032945 -id:A032945 - cp's OEIS frontend

A061479 Smallest number m such that first digit - second digit + third digit - fourth digit ... (of m) = n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 109, 209, 309, 409, 509, 609, 709, 809, 909, 10909, 20909, 30909, 40909, 50909, 60909, 70909, 80909, 90909, 1090909, 2090909, 3090909, 4090909, 5090909, 6090909, 7090909, 8090909, 9090909, 109090909, 209090909

Offset: 0

Amarnath Murthy, May 05 2001

			a(14) = 509 as 5-0+9 =14 and it is the smallest such number.

Subsequence of A032945.

Cf. A225693, A008593, A060978-A060980, A060982, A061470-A061478, A061870-A061882.

m = 0; Do[ While[ a = IntegerDigits[ m ]; l = Length[ a ]; e = o = {}; Do[ o = Append[ o, a[ [ 2k - 1 ] ] ], {k, 1, l/2 + .5} ]; Do[ e = Append[ e, a[ [ 2k ] ] ], {k, 1, l/2} ]; Abs[ Apply[ Plus, o ] - Apply [ Plus, e ] ] != n, m++ ]; Print[ m ], {n, 1, 50} ]

More terms from Robert G. Wilson v, May 10 2001

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

Original entry on oeis.org

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

Offset: 1

Eric Angelini, Jan 30 2014

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

			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

T. D. Noe, Table of n, a(n) for n = 1..8495 (terms < 10^6)

Cf. A236403 (complement).

Cf. A198298, A203565, A203566, A203569.

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 *)

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

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

a(n) ~ n. - Charles R Greathouse IV, Jan 30 2014

A252480 Numbers whose decimal representation has at least one '0' digit in a position other than the final digit.

Original entry on oeis.org

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, 408, 409, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 600, 601, 602, 603, 604, 605, 606

Offset: 1

M. F. Hasler, Dec 28 2014

Similar but different sequences are the "Cyclops numbers" A134808 and A032945 and A051022, which are subsequences, except for the 1- and 2-digit terms.
Also, numbers whose decimal representation cannot be split up between any two digits without producing a string with a leading zero (other than "0" itself).
Also, numbers n > 9 such that floor(n/10) is in A011540, i.e., has a digit '0'.

M. F. Hasler, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Select[Range[10,700],DigitCount[Floor[#/10],10,0]>0&] (* Harvey P. Dale, May 10 2020 *)

PARI
```
is(n)=n>9 && !vecmin(digits(n\10))
```

cp's OEIS Frontend

A061479 Smallest number m such that first digit - second digit + third digit - fourth digit ... (of m) = n.

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

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A252480 Numbers whose decimal representation has at least one '0' digit in a position other than the final digit.

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