A130199 Evil oblong (promic) numbers.

0, 6, 12, 20, 30, 72, 90, 132, 156, 210, 240, 272, 306, 380, 420, 462, 600, 650, 756, 870, 1056, 1122, 1260, 1406, 1482, 1560, 1806, 1892, 1980, 2070, 2256, 2352, 2550, 2652, 3192, 3422, 3660, 3906, 4032, 4160, 4290, 4556, 4830, 5112, 5256, 5402, 5550, 5852

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2*A130200(n). Multiplying by 2 doesn't change evilness. Hence evil oblong numbers are twice evil triangular numbers.

Example

6 belongs to the sequence because binary expansion of 6 is 110 - contains an even number of ones.

Mathematica

Select[Table[n(n + 1), {n, 0, 100}], EvenQ[Plus @@ IntegerDigits[ #, 2]] &]

Prog

(PARI) is(n)=n%2==0 && hammingweight(n)%2==0 && ispolygonal(n/2, 3) \\ Charles R Greathouse IV, Mar 16 2022

Crossrefs

Cf. This sequence is the intersection of evil numbers (A001969) and oblong numbers (A002378).

Sequence in context: A056930 A326378 A064971 * A295904 A309836 A117343

Adjacent sequences: A130196 A130197 A130198 * A130200 A130201 A130202

Keyword

nonn,easy

Author

Tanya Khovanova, May 16 2007

Extensions

a(1) = 0 inserted and offset corrected by Amiram Eldar, Dec 09 2019

Status

approved