A127256 a(n) is the initial element of the sequence A(n) defined exactly like A119751 but with the additional condition that each of its elements must not be contained in any of the sequences A(k) for k < n.

1, 5, 15, 23, 33, 41, 53, 75, 89, 99, 105, 113, 153, 155, 165, 189, 215, 239, 249, 261, 281, 293, 323, 341, 363, 371, 375, 405, 411, 419, 431, 473, 519, 543, 545, 561, 575, 629, 659, 699, 725, 741, 743, 765, 785, 803, 831, 849, 893, 905, 915, 923, 933, 935

Offset

1,2

Comments

a(n)=A(n,1), the first element of each sequence A(n) defined recursively as follows. Recall that A119751 is the sequence defined recursively by a(1)=1 and a(k) is the first odd number greater than a(k-1) such that 2a(k)+1 is prime and a(k)+a(j)+1 is prime for all 1<=j<k. Let A(1)=A119751, that is, A(1,k)=A119751(k). Then A(n) is the sequence defined recursively as follows: (1) A(n,1) is the first odd number not in any A(m), 1<=m<n, such that 2A(n,1)+1 is prime. (2) A(n,k) is the first odd number greater than A(n,k-1), not in any A(m), 1<=m<n, such that 2A(n,k)+1 is prime. (3) A(n,k)+A(n,j)+1 is prime for all 1<=j<k.

Links

Table of n, a(n) for n=1..54.

Example

a(1)=1 is the first element of A119751=1, 3, 9, 69, 429, 4089, 86529, 513099, ... so a(2)=5 since 5 is the first odd number not in A119751 such that 2*5+1 is prime. Furthermore, A(2)=5, 11, 35, 95, 221, 551, 1271, 5705,...

Crossrefs

Cf. A119751, A119752, A127257.

Sequence in context: A328249 A110702 A141394 * A136139 A029480 A029504

Adjacent sequences: A127253 A127254 A127255 * A127257 A127258 A127259

Keyword

nonn

Author

Walter Kehowski, Jan 10 2007

Status

approved