A132435 Composite integers n with two prime factors nearly equidistant from the integer part of the square root of n.

4, 6, 9, 10, 14, 22, 25, 35, 49, 55, 65, 77, 85, 91, 119, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 361, 377, 391, 407, 437, 493, 527, 529, 551, 589, 629, 667, 697, 703, 713, 841, 851, 899, 943, 961, 989, 1073, 1081, 1147, 1189

Offset

1,1

Comments

An integer n is included if, for some value y >= 0: n = A007918(A000196(n) + y) * A007918(A000196(n) - y) Or: n = nextprime(sqrtint(n) + y) * nextprime(sqrtint(n) - y) Where "nextprime(x)" is the smallest prime number >= to x and "sqrtint(z)" is the integer part of the square root of z.

Has many terms in common with A078972. - Bill McEachen, Dec 24 2020

Links

Michel Marcus, Table of n, a(n) for n = 1..3406

Example

25 = nextprime(5 + 0) * nextprime(5 - 0) = 5 * 5 = 25
35 = nextprime(5 + 1) * nextprime(5 - 1) = 7 * 5 = 35
119 = nextprime(10 + 4) * nextprime(10 - 4) = 17 * 7 = 119

Prog

(PARI) bal(x, y) = nextprime(sqrtint(x)+y) * nextprime(sqrtint(x)-y);
findbal(x) = local(z, y); z=sqrtint(x); while( 0<=z, y=bal(x, z); if(y==x, print1(x", "); break; ); z--; );
for (n=1, 1200, findbal(n));

Crossrefs

Cf. A007918, A000196, A078972.

Sequence in context: A054395 A142863 A318990 * A108631 A200677 A189553

Adjacent sequences: A132432 A132433 A132434 * A132436 A132437 A132438

Keyword

nonn

Author

Andrew S. Plewe, Nov 13 2007

Status

approved