A111186 Difference between the closest squares surrounding nonsquare composite numbers.

5, 5, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19

Offset

1,1

Links

Table of n, a(n) for n=1..65.

Formula

Let k be a nonsquare composite number and r = floor(sqrt(k)). Then the closest surrounding squares of k are r^2 and (r+1)^2. So d = (r+1)^2 - r^2 = 2*r+1.

Example

6 is the first nonsquare composite number. 2^2 and 3^2 are the closest squares surrounding 6. So the difference, 9-4 = 5, is the first entry in the table.

Prog

(PARI) surrsq(n) = { local(r, d); for(x=1, n, if(!issquare(x)&!isprime(x), r=sqrtint(x); d=r+r+1; print1(d", ") ) ) }

Crossrefs

Cf. A089229.

Sequence in context: A231589 A133888 A244587 * A384502 A127798 A053671

Adjacent sequences: A111183 A111184 A111185 * A111187 A111188 A111189

Keyword

easy,nonn

Author

Cino Hilliard, Nov 12 2005

Extensions

Name and offset corrected by Jason Yuen, Jan 06 2026

Status

approved