126 Jean-Marie De Koninck
1 352
the only solution n
1012
of σ(n) = 2n + 41 (see the number 196).
1 361
the smallest prime number that is preceded by 33 consecutive composite num-
bers; indeed, there are no prime numbers between 1 327 and 1 361;
the third prime number obtained by the Mills formula qk =
[θ3k
]: indeed,
Mills [136] proved that there exists a real number θ such that
[θ3k
] is a prime
number for k = 1, 2, 3, . . ., this constant being θ = 1.30637788386308069 . . .:
the first four terms of the sequence of numbers (qk)k≥1 are: 2, 11, 1 361 and
2 521 008 887.
1 364
the fifth solution of σ(n) = σ(n + 1) (see the number 14).
1 367
the smallest prime factor of the Mersenne number
2683
1;
the eighth prime number p such that
(3p
1)/2 is itself a prime number (see
the number 1 091).
1 368
the number of ways one can fold a 3 × 3 stamp sheet: for n = 1, 2, 3, 4, 5,
the number of ways one can fold an n × n stamp sheet is 1, 8, 1 368, 300 608,
186 086 600, respectively (see Sloane & Plouffe [188], sequence M4587).
1 375
the smallest number which is the first of three consecutive numbers each being
divisible by a cube 1: 1 375 =
53
· 11, 1 376 =
25
· 43, 1 377 =
34
· 17; if nk
stands for the smallest number which is the first of three consecutive numbers
each being divisible by a
kth
power, then n2 = 48, n3 = 1 375, n4 = 33 614,
n5 = 2 590 623, n6 = 26 890 623 and n7 = 2 372 890 624;
the largest known number n such that γ(n + 1) γ(n) = 31; the only solutions
n 109 of this equation are 32, 36, 40, 45, 60 and 1 375 (see the number 98).
1 385
the eighth Euler number (see the number 272).
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