A134999 -id:A134999 - cp's OEIS frontend

A135999 Numbers that are both triangular numbers A000217 and triangle-shaped numbers A134999.

105, 120, 136, 153, 171, 190, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 703, 780, 820, 861, 903, 946, 990, 1596, 1711, 2145, 2346, 3240, 3321, 3486, 3570, 3741, 4371, 4560, 4753, 5565

Offset: 1

Omar E. Pol, Dec 10 2007

The number 496 appears to be the unique perfect number A000396 of this sequence. The interesting numbers 120 and 153 are supertriangular numbers.

			The numbers 120 as a triangle-shaped number A134999:
. 2 .
1 . .
. . 0
The number 120 as a triangular number A000217:
. . . . . . . O
. . . . . . .O O
. . . . . . O O O
. . . . . .O O O O
. . . . . O O O O O
. . . . .O O O O O O
. . . . O O O O O O O
. . . .O O O O O O O O
. . . O O O O O O O O O
. . .O O O O O O O O O O
. . O O O O O O O O O O O
. .O O O O O O O O O O O O
. O O O O O O O O O O O O O
.O O O O O O O O O O O O O O
O O O O O O O O O O O O O O O <--- A000217(15)=120.

Cf. A000217, A000396, A134999, A135600, A135601, A135602, A135603, A135643.

A301516 Numbers n with decimal expansion (d_1, ..., d_k) such that the convex hull of the set of points { (i, d_i), i = 1..k } has positive area.

Original entry on oeis.org

100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 154, 155

Offset: 1

Rémy Sigrist, Dec 16 2018

This sequence is the complement of the straight-line numbers (0..99 alongside A135643).

This sequence first differs from A134999 at n = 857: a(857) = 1001 whereas A134999(857) = 1011.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A134999, A135643, A302907.

is(n, base=10) = my (d=digits(n, base)); for (i=1, #d-2, if (d[i]+d[i+2]-2*d[i+1], return (1))); return (0)

def ok(n):
    d = list(map(int, str(n)))
    return any(d[i]+d[i+2]-2*d[i+1] != 0 for i in range(len(d)-2))
print([k for k in range(1002) if ok(k)]) # Michael S. Branicky, Aug 03 2022 after Rémy Sigrist

cp's OEIS Frontend

A135999 Numbers that are both triangular numbers A000217 and triangle-shaped numbers A134999.

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A301516 Numbers n with decimal expansion (d_1, ..., d_k) such that the convex hull of the set of points { (i, d_i), i = 1..k } has positive area.

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