A241662 Numbers of the form m * 10^k where gcd(10, m) = 1 and k >= 0 and m > 0.

1, 3, 7, 9, 10, 11, 13, 17, 19, 21, 23, 27, 29, 30, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 70, 71, 73, 77, 79, 81, 83, 87, 89, 90, 91, 93, 97, 99, 100, 101, 103, 107, 109, 110, 111, 113, 117, 119, 121, 123, 127, 129, 130, 131, 133

Offset

1,2

Comments

Also natural numbers x such that fractions of the form x/10^r, after reduction to lowest terms, still have a power of ten in the denominator.

Superset of A045572, and every member of a(n) arises from a member of A045572 by appending zero or more '0' digits at the right.

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = 9n/4 + O(log n). - Charles R Greathouse IV, May 14 2014

Example

19/10 is already fully reduced, and has a power of 10 in its denominator, so 19 is in the sequence;
30/100 reduces to 3/10, which has a power of 10 in its denominator, so 30 is in the sequence;
12/10, 15/100, and 20/100 reduce to 6/5, 3/20, and 1/5, respectively (none of which has a power of 10 in its denominator), so 12, 15, and 20 are not in the sequence.

Prog

(PARI) for(i=1, 400, if(valuation(i, 2)==valuation(i, 5), print1(i, ", ")))
(PARI) is(n)=gcd(n/10^valuation(n, 10), 10)==1 \\ Charles R Greathouse IV, May 14 2014

Crossrefs

Cf. A064615 (uses 6 instead of 10).

Sequence in context: A326911 A037372 A194407 * A097475 A177732 A081339

Adjacent sequences: A241659 A241660 A241661 * A241663 A241664 A241665

Keyword

nonn,easy

Author

Jeppe Stig Nielsen, Apr 26 2014

Status

approved