A329338 a(n) = {1{0}^(A268336(n)-1)}^(n-1){1}{0}^A051903(n): upper bound for A329126(n).

1, 110, 101010, 111100, 100010001000100010, 1111110, 10000010000010000010000010000010000010, 11111111000, 1010101010101010100, 10101010101010101010, 100000000010000000001000000000100000000010000000001000000000100000000010000000001000000000100000000010

Offset: 1

Author

M. F. Hasler, Nov 13 2019

Keywords

• nonn

Comments

This is the upper bound for A329126 as explained in the "FORMULA" there.

It is sharp for all n except 10, 14, 15, ...

Crossrefs

Cf. A329126, A329000, A329339 (this converted from binary to decimal), A268336, A051903.

Programs

PARI

apply( {A329338(n)=my(k=lcm(lcm([p-1|p<-factor(n)[,1]]), n)/n); fromdigits(concat(vector(n, i, Vec(1, if(i1, vecmax(factor(n)[,2])+1)))))}, [1..16])

Formula

a(n) = A007088(A329339(n)), where A007088 = binary numbers and A329339(n) = 2^A051903(n)*(m^n-1)/(m-1) with m = 2^A268336(n).