A099502 Numbers n such that A099501(n) = 3.

3, 13, 20, 78, 85, 92, 99, 109, 136, 139, 143, 146, 150, 358, 402, 440, 457, 477, 501, 546, 549, 583, 611, 638, 655, 665, 696, 730, 754, 778, 812, 887, 904, 966, 979, 996, 1034, 1051, 2089, 2161, 2427, 2458, 2499, 2697, 2751, 2813, 2840, 2912, 2922, 2929

Offset

1,1

Comments

Granville and Selfridge discuss the numbers n+1 in their paper. For each of these n<10000, Scott Contini found three integers between n^2 and (n+1)^2 such that their product is twice a square. There are 123 instances of n < 10000; 215 instances for n < 20000.

Links

Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..516 (terms < 10^5, first 367 terms from Donovan Johnson)

Andrew Granville and John Selfridge, Product of integers in an interval, modulo squares, Electronic Journal of Combinatorics, Volume 8(1), 2001.

Giovanni Resta, Table of n, a(n), x, y, z, where x, y, z is the triple corresponding to a(n)<10^5

Example

13 is here because {171,180,190} is the smallest set of integers in the interval [170,195] whose product is twice a square.

Crossrefs

Cf. A099500 (number of subsets), A099501 (size of the subset having the least number of integers).

Sequence in context: A273686 A215567 A214519 * A145024 A055059 A050903

Adjacent sequences: A099499 A099500 A099501 * A099503 A099504 A099505

Keyword

hard,nonn

Author

T. D. Noe, Oct 20 2004

Status

approved