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 A277375 Each nonprime integer "n" is followed by n prime integers. 1
 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, 79, 83, 89, 97, 101, 103, 107, 10, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. From Michael De Vlieger, Oct 12 2016 (Start): Each nonprime c = A018252(n) followed by c primes starting with prime(A175967(n)). The position of nonprimes in a(n) is {1, 3, 8, 15, 24, 34, 45, 58, 73, 89, 106, 125, ...}. (End) LINKS Jean-Marc Falcoz, Table of n, a(n) for n = 1..7162 EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A018252 (nonprimes), A175967. Sequence in context: A238980 A327143 A082006 * A232798 A155850 A134464 Adjacent sequences:  A277372 A277373 A277374 * A277376 A277377 A277378 KEYWORD nonn,base AUTHOR Eric Angelini and Jean-Marc Falcoz, Oct 11 2016 STATUS approved

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Last modified April 1 02:15 EDT 2020. Contains 333153 sequences. (Running on oeis4.)