A135643 Straight-line numbers > 99.

111, 123, 135, 147, 159, 210, 222, 234, 246, 258, 321, 333, 345, 357, 369, 420, 432, 444, 456, 468, 531, 543, 555, 567, 579, 630, 642, 654, 666, 678, 741, 753, 765, 777, 789, 840, 852, 864, 876, 888, 951, 963, 975, 987, 999, 1111, 1234

Offset

1,1

Comments

Numbers with more than two digits whose digits are in arithmetic progression. The structure of digits represents a straight line. In the graphic representation the points are connected by imaginary line segments. For a(1) to a(45) this sequence is equal to A034840. Each term of this sequence that is greater than 9876543210 is a repdigit number (A010785).

Note that the sequence of straight-line numbers starts: 10, 11, 12, ..., 98, 99, 111, 123, ... All 2-digit numbers are straight-line numbers, but here the numbers < 100 are omitted. - Omar E. Pol, Nov 14 2009

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..168

Example

The number 3579 is a straight-line number:
  . . . 9
  . . . .
  . . 7 .
  . . . .
  . 5 . .
  . . . .
  3 . . .
  . . . .
  . . . .
  . . . .

Mathematica

Select[Range[100, 1300], Length[Union[Differences[IntegerDigits[#]]]]==1&] (* Harvey P. Dale, May 09 2012 *)

Prog

(Haskell)
a135643 n = a135643_list !! (n-1)
a135643_list = filter f [100..] where
   f x = all (== 0) ws where
         ws = zipWith (-) (tail vs) vs
         vs = zipWith (-) (tail us) us
         us = map (read . return) $ show x
-- Reinhard Zumkeller, Sep 21 2014
(PARI) is(n) = my (d=digits(n), cvx=0, ccv=0, str=0); for (i=1, #d-2, my (x=d[i]+d[i+2]-2*d[i+1]); if (x>0, cvx++, x<0, ccv++, str++)); return (cvx==0 && ccv==0 && str>0) \\ Rémy Sigrist, Aug 09 2017
(Python)
from itertools import count, islice
def agen():
    progressions = ["".join(map(str, range(i, j+1, d))) for i in range(10) for d in range(1, 10-i) for j in range(i+2*d, 10)]
    s =  [p for p in progressions if p[0] != "0"]          # up
    s += [p[::-1] for p in progressions]                   # down
    s += [d*i for d in "123456789" for i in range(3, 11)]  # flat
    yield from sorted(set(int(w) for w in s))
    yield from (int(f*d) for d in count(11) for f in "123456789")
print(list(islice(agen(), 178))) # Michael S. Branicky, Aug 03 2022

Crossrefs

Cf. A010785, A034840.

Cf. A135600, A135601, A135602, A135603, A135641, A135642, A163278, A167847. - Omar E. Pol, Nov 14 2009

Cf. A247616 (subsequence).

Sequence in context: A280732 A280636 A034840 * A070798 A235039 A279423

Adjacent sequences: A135640 A135641 A135642 * A135644 A135645 A135646

Keyword

nonn,base

Author

Omar E. Pol, Nov 30 2007, Dec 09 2008, Nov 14 2009

Status

approved