Those Fascinating Numbers 117

n9 = 14 926 249 =

23

+

343

+

2463

=

123

+

1863

+

2043

=

153

+

333

+

2463

=

513

+

1143

+

2373

=

723

+

903

+

2403

=

753

+

1903

+

1973

=

903

+

1863

+

1983

=

993

+

1493

+

2203

=

1063

+

1503

+

2183,

n10 = 34 012 224 =

363

+

2163

+

2883

=

393

+

1533

+

3123

=

413

+

1143

+

3193

=

453

+

2463

+

2673

= 723 + 1143 + 3183 = 1003 + 1923 + 2963

= 1023 + 2273 + 2773 = 1183 + 1863 + 2963

= 1623 + 2163 + 2703 = 1733 + 2143 + 2673.

1 019

• the eighth prime number pk such that p1p2 . . . pk + 1 is prime (see the number

379).

1 021

• the ninth prime number pk such that p1p2 . . . pk + 1 is prime (see the number

379).

1 030

• the third number n such that σ(n) = σ(n + 5); the sequence of numbers sa-

tisfying this property begins as follows: 6, 46, 1030, 2673, 4738, 4785, 10437,

14025, 20038, 20326, 23914, 28702, . . .

1 031

• the fifth number k such that 11 . . . 1

k

is prime (H.C. Williams & H. Dubner [206]);

see the number 19.

1 037

• the smallest composite Phibonacci number; we say that a number n ≥ 3 is a

Phibonacci number if

φ(n) = φ(n − 1) + φ(n − 2);

the only composite Phibonacci numbers 106 are 1 037, 1 541, 6 527, 9 179,

55 387, 61 133, 72 581, 110 177, 152 651, 179 297, 244 967, 299 651, 603 461 and

619 697; this notion was introduced by A. Bager [9] in 1981.