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

1,1

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.

Links

Table of n, a(n) for n=1..20.

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]).

Example

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

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 *)

Crossrefs

Cf. A003015.

Sequence in context: A155710 A001491 A112352 * A168513 A067598 A043683

Adjacent sequences: A298469 A298470 A298471 * A298473 A298474 A298475

Keyword

nonn

Author

Christopher E. Thompson, Jan 19 2018

Status

approved