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A135643 Straight-line numbers > 99. 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers with more than two digits whose digits are in arithmetic progression. The structure of digits represent 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. If the member of this sequence is greater than 9876543210 then the member is a repdigit number A010785.

Note that the sequence of straight-line numbers starts: 10, 11, 12, ..., 98, 99, 111, 123, ... The integers with 2 digits are always 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

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: A280636 A039990 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

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Last modified October 22 12:22 EDT 2018. Contains 316446 sequences. (Running on oeis4.)