A298472 Numbers n such that n and n-1 are both nontrivial binomial coefficients.

21, 36, 56, 253, 496, 561, 1771, 2926, 3655, 5985, 26335, 2895621, 2919736, 6471003, 21474181, 48792381, 346700278, 402073903, 1260501229261, 12864662659597529

Offset: 1

Author

Christopher E. Thompson, Jan 19 2018

Keywords

• nonn

Comments

Nontrivial here means binomial(r,s) with 2 <= s <= r-2 (or the sequence would be uninteresting).

Blokhuis et al. show that the values given are complete up to 10^30, and conjecture that there are no more.

Examples

			binomial(6,3)=20 and binomial(7,2)=binomial(7,5)=21 are the smallest adjacent pair, so a(1)=21.
		

Links

• Aart Blokhuis, Andries Brouwer, Benne de Weger, Binomial collisions and near collisions, INTEGERS, Volume 17, Article A64, 2017 (also available as arXiv:1707.06893 [math.NT]).

Crossrefs

Cf. A003015.

Programs

Mathematica

nmax = 1000; t = Table[Binomial[n, k], {n, 4, nmax}, {k, 2, Floor[n/2]}] // Flatten // Sort // DeleteDuplicates; Select[Split[t, #2 == #1+1&], Length[#] > 1&][[All, 2]] (* Jean-François Alcover, Feb 20 2018 *)