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A135642 Concave numbers. 11
110, 120, 121, 122, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 158, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The structure of digits represent a concave function or a concave object. In the graphic representation the points are connected by imaginary line segments (or line curves) from left to right.

Only strictly concave numbers are included in this sequence; the interpolation between at least one pair of digits must be strictly less than some intermediate digit. - Franklin T. Adams-Watters, Jan 26 2014

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

The number 12221 is a concave number. Note that the number of this sequence (A135642) is also a concave number as shown below:

.

9     . . . . . .      . . . . . .

8     . . . . . .      . . . . . .

7     . . . . . .      . . . . . .

6     . . . x . .      . . . 6 . .

5     . . x . . .      . . 5 . . .

4     . . . . x .      . . . . 4 .

3     . x . . . .      . 3 . . . .

2     . . . . . x      . . . . . 2

1     x . . . . .      1 . . . . .

0     . . . . . .      . . . . . .

.

Another example is 1342. On the other hand 3124 is not in the sequence, it's in A135641. 1234 is not in the sequence, it's in A135643. 1243 is not in the sequence, it's in A163278. - Omar E. Pol, Jan 29 2014

PROG

(PARI) { isconcave(n) = my(t, r); t=eval(Vec(Str(n))); r=0; for(i=1, #t, for(j=i+2, #t, for(k=i+1, j-1, if( t[k]*(j-i) < t[i]*(j-k) + t[j]*(k-i), return(0)); if( t[k]*(j-i) > t[i]*(j-k) + t[j]*(k-i), r=1); ))); r } /* Max Alekseyev, Jan 30 2014 */

CROSSREFS

Cf. A135600, A135601, A135602, A135603, A135641, A135643, A163278.

Sequence in context: A182621 A036230 A171236 * A166323 A194429 A084042

Adjacent sequences:  A135639 A135640 A135641 * A135643 A135644 A135645

KEYWORD

nonn,base

AUTHOR

Omar E. Pol, Nov 30 2007

EXTENSIONS

PARI code corrected per Franklin T. Adams-Watters's suggestion by Max Alekseyev, Jan 30 2014

STATUS

approved

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Last modified December 20 13:53 EST 2014. Contains 252266 sequences.