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%I #20 Oct 29 2016 13:27:15
%S 1,2,4,3,5,7,11,6,13,17,19,23,29,31,8,37,41,43,47,53,59,61,67,9,71,73,
%T 79,83,89,97,101,103,107,10,109,113,127,131,137,139,149,151,157,163,
%U 12,167,173,179,181,191,193,197,199,211,223,227,229,14,233,239,241,251,257,263,269,271,277,281,283,293,307,311,15,313
%N Each nonprime integer "n" is followed by n prime integers.
%C The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
%C From _Michael De Vlieger_, Oct 12 2016 (Start):
%C Each nonprime c = A018252(n) followed by c primes starting with prime(A175967(n)).
%C The position of nonprimes in a(n) is {1, 3, 8, 15, 24, 34, 45, 58, 73, 89, 106, 125, ...}. (End)
%H Jean-Marc Falcoz, <a href="/A277375/b277375.txt">Table of n, a(n) for n = 1..7162</a>
%e As a(1) = 1, we take for a(2) the prime "2"; we then extend the sequence with a(3) which must be the smallest nonprime not yet present: this is "4"; we take for a(4), a(5), a(6) and a(7) the 4 smallest primes not yet present: they are 3, 5, 7 and 11; we then extend the sequence with the smallest nonprime available, which is a(8) = 6. Etc.
%t c = Select[Range@ 120, ! PrimeQ@ # &]; Table[Prepend[Prime@ Most[Range @@ Take[FoldList[Plus, 0, Take[c, n]] + 1, -2]], c[[n]]], {n, 9}] // Flatten (* _Michael De Vlieger_, Oct 12 2016 *)
%Y Cf. A018252 (nonprimes), A175967.
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Oct 11 2016
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