A060982 a(n) = Smallest nontrivial number k > 9 such that |first (leftmost) decimal digit of k - second digit + third digit - fourth digit ...| = n.

11, 10, 13, 14, 15, 16, 17, 18, 19, 90, 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, 309090909

Offset: 0

Author

Robert G. Wilson v, May 10 2001

Keywords

• base
• nonn
• easy

Comments

Starting with 109, this sequence has the same terms as A061479 and A061882. - Georg Fischer, May 24 2022

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..4500

Crossrefs

Cf. A008593, A060978-A060980, A060982, A061470-A061479, A061870-A061882.

Programs

Mathematica

m = 2; 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} ]

Python

def f(m): return abs(sum((-1)**i*int(d) for i, d in enumerate(str(m))))
def a(n):
    m = 10
    while f(m) != n: m += 1
    return m
print([a(n) for n in range(28)]) # Michael S. Branicky, Nov 10 2021

Python

# faster version based on formula
def a(n):
    if n < 10: return [11, 10, 13, 14, 15, 16, 17, 18, 19, 90][n]
    q, r = divmod(n, 9)
    return int(str(r if r else 9) + "09"*(q if r else q-1))
print([a(n) for n in range(40)]) # Michael S. Branicky, Nov 10 2021

Formula

For n > 8, if r = 0, a(n) = 90..90, else a(n) = r09..09, where r = n mod 9 and 90 and 09, resp., occur ceiling(n/9) times. - Michael S. Branicky, Nov 10 2021

Extensions

a(39) and beyond from Michael S. Branicky, Nov 10 2021

Definition amended by Georg Fischer, May 24 2022