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A135641
Convex numbers.
10
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
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
KEYWORD
nonn,base
AUTHOR
Omar E. Pol, Nov 30 2007
STATUS
approved