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Distinct terms in A251416.
4

%I #8 Apr 30 2024 23:08:44

%S 2,3,4,5,6,7,10,11,13,17,18,19,23,29,31,37,41,43,47,53,59,61,67,71,73,

%T 79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,

%U 173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257

%N Distinct terms in A251416.

%C A251417(n) gives number of repetitions of a(n) in A251416;

%C a(n) = prime(n-4) for n > 11 according to Bradley Klee's conjecture, empirically confirmed for the first 10000 primes;

%C equivalently: A098551(a(n)) = A251239(n-4) for n > 11.

%H Reinhard Zumkeller, <a href="/A251595/b251595.txt">Table of n, a(n) for n = 1..10000</a>

%e . n | a(n) | A151417(n) | A098551(a(n))

%e . ----+--------------+------------+--------------

%e . 1 | 2 | 1 | 2

%e . 2 | 3 | 1 | 3

%e . 3 | 4 = 2*2 | 1 | 4

%e . 4 | 5 | 5 | 9

%e . 5 | 6 = 2*3 | 1 | 10

%e . 6 | 7 | 5 | 15

%e . 7 | 10 = 2*5 | 1 | 16

%e . 8 | 11 | 6 | 22

%e . 9 | 13 | 1 | 23

%e . 10 | 17 | 7 | 30

%e . 11 | 18 = 2*3*3 | 1 | 31

%e . 12 | 19 | 12 | 43

%e . 13 | 23 | 8 | 51

%e . 14 | 29 | 10 | 61

%e . 15 | 31 | 1 | 62

%e . 16 | 37 | 17 | 79

%e . 17 | 41 | 8 | 87

%e . 18 | 43 | 1 | 88

%e . 19 | 47 | 13 | 101

%e . 20 | 53 | 13 | 114

%e . 21 | 59 | 13 | 127

%e . 22 | 61 | 5 | 132

%e . 23 | 67 | 10 | 142

%e . 24 | 71 | 11 | 153

%e . 25 | 73 | 5 | 158

%e The last column gives the position of a(n) in A098550.

%o (Haskell)

%o import Data.List (group)

%o a251595 n = a251595_list !! (n-1)

%o a251595_list = map head $ group a251416_list

%Y Cf. A098550, A098551, A251416, A251417, A251239.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 05 2014