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A298472
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Numbers n such that n and n-1 are both nontrivial binomial coefficients.
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0
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21, 36, 56, 253, 496, 561, 1771, 2926, 3655, 5985, 26335, 2895621, 2919736, 6471003, 21474181, 48792381, 346700278, 402073903, 1260501229261, 12864662659597529
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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binomial(6,3)=20 and binomial(7,2)=binomial(7,5)=21 are the smallest adjacent pair, so a(1)=21.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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