A002251 -id:A002251 - cp's OEIS frontend

A086482 Beginning with 1, the smallest number not included earlier such that the n-th partial product is an n-th power; or the geometric mean of the first n terms is an integer.

1, 4, 2, 32, 128, 8, 1024, 16, 8192, 32768, 64, 262144, 1048576, 256, 8388608, 512, 67108864, 268435456, 2048, 2147483648, 4096, 17179869184, 68719476736, 16384, 549755813888, 2199023255552, 65536, 17592186044416, 131072, 140737488355328

Offset: 1

Amarnath Murthy, Jul 26 2003

nonn

Every term is a power of 2 and the geometric mean of first n terms is 2 for n >1. Rearrangement of powers of 2.

			a(5) = 128: the product of the first five terms is 1*4*2*32*128 = 2^15 = 8^5; 4 gives 4^5, also a 5th power, but 4 is already included.

Cf. A002251.

v=[1];n=1;while(n<10^4,p=n*prod(i=1,#v,v[i]);if(ispower(p,#v+1)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=1);n++);v \\ Derek Orr, May 27 2015

a(n) = 2^A002251(n-1). - David Wasserman, Mar 07 2005

More terms from David Wasserman, Mar 07 2005

A115094 Permutation of N based on lower Wythoff sequence.

Original entry on oeis.org

3, 2, 1, 6, 5, 4, 7, 9, 8, 10, 12, 11, 13, 16, 15, 14, 19, 18, 17, 20, 22, 21, 23, 25, 24, 26, 29, 28, 27, 32, 31, 30, 35, 34, 33, 36, 38, 37, 39, 42, 41, 40, 45, 44, 43, 48, 47, 46, 49, 51, 50, 52, 55, 54, 53, 58, 57, 56, 61, 60, 59, 62, 64, 63, 65, 67, 66, 68, 71, 70, 69, 74

Offset: 1

Clark Kimberling, Mar 02 2006

nonn

(1) a(n)=n if and only if n is in the upper Wythoff sequence, A001950. (2) This is a self-inverse permutation of N. (3) a(n)-n is one of -2,-1,0,1,2 for every n and each of these occurs infinitely many times. (4) The sequence a(n)-n is a nonperiodic tiling of N.

			a(1)=3=L(1+1) because 1=L(1).
a(2)=2 because 2 is not in L.
a(3)=1=L(2-1) because 3=L(2).
a(4)=6=L(3+1) because 4=L(3).
a(6)=4=L(4-1) because 6=L(4).

Cf. A000201, A001950, A002251.

Let L be the lower Wythoff sequence, A000201. Then a(n)=n if n is not any L(k), a(n)=L(k+1) if n=L(k) for odd k, a(n)=L(k-1) if n=L(k) for even k.

cp's OEIS Frontend

A086482 Beginning with 1, the smallest number not included earlier such that the n-th partial product is an n-th power; or the geometric mean of the first n terms is an integer.

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