A396581 The fractional part of A000037(n) is the a(n)-th smallest fractional part of all sqrt(m) where m is nonsquare and 1 <= m <= A000037(n).

1, 2, 1, 3, 4, 6, 1, 3, 6, 7, 10, 12, 1, 4, 6, 10, 11, 14, 17, 20, 1, 4, 7, 10, 15, 16, 20, 24, 27, 30, 1, 5, 9, 12, 15, 21, 22, 26, 30, 34, 38, 42, 1, 5, 9, 13, 17, 22, 28, 29, 34, 38, 44, 47, 52, 56, 1, 6, 10, 16, 19, 24, 29, 36, 37, 42, 48, 52, 57, 63, 67, 72

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10100

Example

a(5) = 4 as A000037(5) = 7 and the nonsquare numbers m such that 1 <= m <= 7 are 2, 3, 5, 6, 7. Listing and sorting the fractional parts of sqrt(m) for these numbers gives [0.23..., 5], [0.41..., 2], [0.44..., 6], [0.64..., 7], [0.73..., 3] and 7 is 4th from the left.

Prog

(PARI) a(n) = {n += (1 + sqrtint(4*n)) \ 2; my(l = List()); for(i = 1, n, if(!issquare(i), listput(l, [frac(sqrt(i)), i]))); listsort(l); select(x->x[2] == n, l, 1)[1]}

Crossrefs

Cf. A000037.

Sequence in context: A029636 A293517 A122514 * A130077 A080412 A300948

Adjacent sequences: A396577 A396579 A396580 * A396582 A396583 A396584

Keyword

nonn

Author

David A. Corneth, May 29 2026

Status

approved