Wendy Appleby - cp's OEIS frontend

A330275 Integers n such that lcm(1, ..., n) > exp(n).

19, 31, 32, 43, 47, 49, 53, 61, 73, 74, 75, 79, 83, 84, 89, 103, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 131, 139, 140, 141, 151, 169, 173, 174, 179, 181, 182, 183, 184, 185, 193, 194, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 211, 233

Offset: 1

Wendy Appleby, Dec 08 2019

nonn

It is well known that lcm(1, ..., n) is approximately exp(n). For most numbers < 100 it is less than exp(n).

Robert Israel, Table of n, a(n) for n = 1..10000
J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics, Vol. 6, No. 1 (1962), pp. 64-94.

Cf. A003418.

[k:k in [1..250]|Lcm([1..k]) gt Exp(k)]; // Marius A. Burtea, Dec 16 2019

select(n -> is(ilcm($1..n) > exp(n)), [$1..300]); # Robert Israel, Dec 08 2019

Select[Range[233], LCM @@ Range[#] > Exp[#] &] (* Amiram Eldar, Dec 08 2019 *)

c=1; for (n=1, 233, c=lcm(c,n); if (c>exp(n), print1 (n", "))) \\ Rémy Sigrist, Dec 08 2019

More terms from Rémy Sigrist, Dec 08 2019

A321511 Number of alternating sign n X n matrices excluding permutation matrices.

Original entry on oeis.org

0, 0, 0, 1, 18, 309, 6716, 213308, 10809896, 911472580, 129530643900, 31095704935575, 12611311380675900, 8639383512070631700, 9995541355360989190800, 19529076234659969430529200, 64427185703425668434106855840, 358869201916137601091798728321296

Offset: 0

Wendy Appleby, Nov 11 2018

nonn

Michael De Vlieger, Table of n, a(n) for n = 0..93
Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
Paul Barry, Extensions of Riordan Arrays and Their Applications, Mathematics (2025) Vol. 13, No. 2, 242. See p. 8.

Cf. A005130.

a[n_] := Product[(3 k + 1)!/(n + k)!, {k, 0, n-1}] - n!; a /@ Range[0, 17] (* Giovanni Resta, Nov 20 2018 *)

a(n) = A005130(n) - n!

A272021 Balanced primes separated from the next lower and next higher prime neighbors by 66.

Original entry on oeis.org

12012743, 12147463, 13408397, 15303667, 32676733, 34460407, 36050293, 36685867, 36804487, 37657423, 41516063, 51146867, 54702367, 56379217, 57203687, 58250207, 60696803, 63699127, 73576067, 74663377, 76853827, 78725443, 82015313, 92438317, 94073923, 94988423

Offset: 1

Wendy Appleby, Apr 18 2016

nonn

This was generated by calculating the first million primes in a spreadsheet, finding their differences and then looking for two consecutive differences equal to 66.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A054342, A058867, A178136.

Prime[Last /@ SequencePosition[ Differences@ Prime@ Range[4 *10^6], {66, 66}]] (* Giovanni Resta, Apr 18 2016 *)

list(lim)=my(v=List(),p=2,q=3); forprime(r=5,nextprime(lim+1), if(q-p==66 && r-q==66, listput(v,q)); p=q;q=r); Vec(v) \\ Charles R Greathouse IV, Apr 18 2016

a(5)-a(26) from Giovanni Resta, Apr 18 2016

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A330275 Integers n such that lcm(1, ..., n) > exp(n).

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A321511 Number of alternating sign n X n matrices excluding permutation matrices.

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A272021 Balanced primes separated from the next lower and next higher prime neighbors by 66.

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