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Lexicographically earliest sequence of distinct composite numbers such that a(k) + a(k+1) is prime for all k.
5

%I #22 Feb 20 2024 07:01:28

%S 4,9,8,15,14,27,10,21,16,25,6,35,12,49,18,55,24,65,32,39,20,33,26,45,

%T 22,51,28,69,34,63,38,75,52,57,40,87,44,93,46,81,50,77,30,119,48,91,

%U 36,95,42,85,54,125,56,111,62,105,58,99,64,115,66,133,60,121,70,123,68,129,82

%N Lexicographically earliest sequence of distinct composite numbers such that a(k) + a(k+1) is prime for all k.

%C Index of composite values: {1, 4, 3, 8, 7, 17, 5, 12, 9, 15, 2, 23, 6, 33, 10, 38, 14, 46, 20, 26, 11, 21, 16, 30, ...}. - _Michael De Vlieger_, Jul 18 2017

%H Michael De Vlieger, <a href="/A075570/b075570.txt">Table of n, a(n) for n = 1..3000</a>

%t a = {4}; Do[k = 2 - Boole@ EvenQ@ n; While[Nand[! MemberQ[a, k], CompositeQ@ k, PrimeQ[a[[n - 1]] + k]], k += 2]; AppendTo[a, k], {n, 2, 69}]; a (* _Michael De Vlieger_, Jul 18 2017 *)

%Y Cf. A025044, A072525, A085084, A240024.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 25 2002

%E More terms from _David Wasserman_, Jan 20 2005

%E Definition clarified by _Peter Munn_, Jul 20 2017