A277375 Each nonprime integer "n" is followed by n prime integers.

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

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: A327143 A343313 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