Braxton Carrigan - cp's OEIS frontend

User: Braxton Carrigan

Braxton Carrigan has authored 2 sequences.

A282164 a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings of length greater than 1.

1, 1, 2, 2, 4, 6, 12, 24, 48, 120, 240, 720, 1440, 4320, 8640, 25920, 60480, 181440, 483840, 1451520, 3870720, 11612160, 34836480, 104509440, 348364800, 1045094400, 3483648000, 10450944000, 38320128000, 114960384000, 459841536000, 1379524608000, 5518098432000, 16554295296000

Offset: 1

Peter Kagey, Braxton Carrigan, Feb 07 2017

nonn

a(n) = sqrt(A282165(n-1)) if A282165(n-1) is square.

			  a(1)  = 1   via [1];
  a(2)  = 1   via [1,1];
  a(3)  = 2   via [1,1,2];
  a(4)  = 2   via [1,1,2,1];
  a(5)  = 4   via [1,1,2,2,1];
  a(6)  = 6   via [1,1,2,1,3,1];
  a(7)  = 12  via [1,1,2,2,1,3,1];
  a(8)  = 24  via [1,1,2,1,3,1,4,1];
  a(9)  = 48  via [1,1,2,2,1,3,1,4,1];
  a(10) = 120 via [1,1,2,1,3,1,4,1,5,1].

Peter Kagey, Table of n, a(n) for n = 1..100

Product analog of A259280.

A274701 First differences of A259280.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8

Offset: 1

Braxton Carrigan, Peter Kagey, Joseph O'Brien, Jul 06 2016

nonn

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A259280, A185869, A002024.

If n is in A185869 then a(n) = ceiling(k) else a(n) = floor(k) where k is (A002024(n) + 1)/2.

cp's OEIS Frontend

User: Braxton Carrigan

A282164 a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings of length greater than 1.

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