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.
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