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

0,1

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

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

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} ]

Prog

(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

Crossrefs

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

Sequence in context: A106421 A019329 A086919 * A324296 A323294 A082122

Adjacent sequences: A060979 A060980 A060981 * A060983 A060984 A060985

Keyword

base,nonn,easy

Author

Robert G. Wilson v, May 10 2001

Extensions

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

Definition amended by Georg Fischer, May 24 2022

Status

approved