A354270 Numbers k such that min{m: A354257(m) = k} = k^2.

1, 3, 4, 5, 6, 7, 11, 12, 13, 15, 17, 19, 20, 21, 23, 28, 29, 30, 31, 33, 35, 37, 39, 41, 42, 43, 44, 47, 51, 52, 53, 55, 57, 59, 60, 61, 65, 66, 67, 68, 69, 71, 73, 76, 77, 78, 79, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 101, 102, 103, 105, 107, 109, 111, 113

Offset

1,2

Comments

Numbers m such that A354258(k) = k^2.

Consists of the union of {squarefree numbers that are odd or congruent to 6 modulo 12} U {4 times odd squarefree numbers}.

The maximum run length of consecutive numbers is 5, and they are of the form 24*m+3..24*m+7 or 24*m+17..24*m+21.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Example

3..7 are terms since the first 3, 4, 5, 6 or 7 in A354257 occur at the 9th, the 16th, the 25th, the 36th or the 49th places respectively.
65..69 are terms since the first 65, 66, 67, 68 or 69 in A354257 occur at the 4225th, the 4356th, the 4489th, the 4624th or the 4761st places respectively.

Prog

(PARI) isA354270(n) = ((n%2 || n%12==6) && issquarefree(n)) || (n%8==4 && issquarefree(n/4))

Crossrefs

Cf. A354257, A354258.

Sequence in context: A039056 A326754 A047562 * A137922 A176984 A099562

Adjacent sequences: A354267 A354268 A354269 * A354271 A354272 A354273

Keyword

nonn,easy

Author

Jianing Song, May 21 2022

Status

approved