cp's OEIS Frontend

A135641 Convex numbers.

%I A135641 #17 Aug 03 2022 02:36:11
%S A135641 100,101,102,103,104,105,106,107,108,109,112,113,114,115,116,117,118,
%T A135641 119,124,125,126,127,128,129,136,137,138,139,148,149,200,201,202,203,
%U A135641 204,205,206,207,208,209,211,212,213,214,215,216,217
%N A135641 Convex numbers.
%C A135641 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.
%H A135641 Rémy Sigrist, <a href="/A135641/b135641.txt">Table of n, a(n) for n = 1..10000</a>
%e A135641 The number 742235 is a convex number.
%e A135641   . . . . . .
%e A135641   . . . . . .
%e A135641   7 . . . . .
%e A135641   . . . . . .
%e A135641   . . . . . 5
%e A135641   . 4 . . . .
%e A135641   . . . . 3 .
%e A135641   . . 2 2 . .
%e A135641   . . . . . .
%e A135641   . . . . . .
%t A135641 convexQ[n_] := With[{dd = IntegerDigits[n]}, AllTrue[SequencePosition[dd, {_, _, _}][[All, 1]], dd[[#]] + dd[[#+2]] > 2 dd[[#+1]]&]];
%t A135641 Select[Range[100, 300], convexQ] (* _Jean-François Alcover_, Nov 01 2018 *)
%o A135641 (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
%Y A135641 Cf. A135642 (concave numbers), A135643 (straight line numbers), A163278 (concave-convex numbers).
%K A135641 nonn,base
%O A135641 1,1
%A A135641 _Omar E. Pol_, Nov 30 2007