A329339 -id:A329339 - cp's OEIS frontend

A329000 a(n) is the least positive number which yields a multiple of n when its binary digit string, S(n), is read in any numeric base; a(n) is displayed in base 10.

1, 6, 42, 60, 139810, 126, 139620524162, 2040, 349524, 419430, 2537779500750160131246576896002, 16380, 44612382091907903486070965589630128805126146, 418861572486, 146602109610, 1048560

Offset: 1

N. J. A. Sloane, Nov 12 2019

If we consider sequence terms to be character strings, a(n) is A329126(n) read in base 2 and converted to base 10. Based on b-file for A329126.

Least k >= 1 such that n divides A329443(k). - Peter Munn, Dec 02 2021

			The strings S(1), S(2), S(3), ... are 1, 110, 101010, 111100, 100010001000100010, 1111110, ... (A329126); converted from binary to decimal these give the current sequence.

Cf. A329126, A329339, A329338, A067029, A268336, A329443.

\\ See A329339. - M. F. Hasler, Nov 14 2019

a(n) <= A329339(n) = 2^A051903(n)*(m^n-1)/(m-1) with m = 2^A268336(n), equality except for n = 10, 14, 15, ... - M. F. Hasler, Nov 14 2019

Definition corrected: not lexicographically earliest string, but smallest binary number. - M. F. Hasler, Nov 09 2021

Name aligned with new A329126 name by Peter Munn, Dec 02 2021

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

Original entry on oeis.org

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

Offset: 1

M. F. Hasler, Nov 13 2019

nonn

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

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

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

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])

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).

cp's OEIS Frontend

A329000 a(n) is the least positive number which yields a multiple of n when its binary digit string, S(n), is read in any numeric base; a(n) is displayed in base 10.

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