A289178 - OEIS

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A289178

Numbers n such that binomial(2*n,n) < (2*n)^pi(n).

3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77

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OFFSET

1,1

COMMENTS

Ecklund and Eggleton proved that binomial(n,k) > n^pi(k) for n >= 2k and k >= 202, where pi(k) = A000720(k). Therefore this sequence is finite.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..104

Earl F. Ecklund, Jr. and Roger B. Eggleton, Prime factors of consecutive integers, The American Mathematical Monthly, Vol. 79, No. 10 (1972), pp. 1082-1089.

MATHEMATICA

binomQ[n_] := Binomial[2n, n] < (2n)^PrimePi[n]; Select[Range[250], binomQ]

PROG

(PARI) isok(n) = binomial(2*n, n) < (2*n)^primepi(n); \\ Michel Marcus, Jun 28 2017

CROSSREFS

Cf. A000720, A000984.

Sequence in context: A039129 A194370 A039092 * A212450 A368828 A047585

Adjacent sequences: A289175 A289176 A289177 * A289179 A289180 A289181

KEYWORD

nonn,fini,full

AUTHOR

Amiram Eldar, Jun 27 2017

STATUS

approved