A135641 Convex numbers.

100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 124, 125, 126, 127, 128, 129, 136, 137, 138, 139, 148, 149, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 211, 212, 213, 214, 215, 216, 217

Offset

1,1

Comments

The structure of digits represents a convex function or a convex object. In the graphic representation the points are connected by imaginary line segments from left to right.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

The number 742235 is a convex number.
  . . . . . .
  . . . . . .
  7 . . . . .
  . . . . . .
  . . . . . 5
  . 4 . . . .
  . . . . 3 .
  . . 2 2 . .
  . . . . . .
  . . . . . .

Mathematica

convexQ[n_] := With[{dd = IntegerDigits[n]}, AllTrue[SequencePosition[dd, {_, _, _}][[All, 1]], dd[[#]] + dd[[#+2]] > 2 dd[[#+1]]&]];
Select[Range[100, 300], convexQ] (* Jean-François Alcover, Nov 01 2018 *)

Prog

(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) \\ Rémy Sigrist, Aug 09 2017

Crossrefs

Cf. A135642 (concave numbers), A135643 (straight line numbers), A163278 (concave-convex numbers).

Sequence in context: A134999 A301516 A204581 * A330859 A252480 A323142

Adjacent sequences: A135638 A135639 A135640 * A135642 A135643 A135644

Keyword

nonn,base

Author

Omar E. Pol, Nov 30 2007

Status

approved