A134292 Triangle in which row n is the lexicographically earliest solution to the prime circle problem for 2n.

1, 2, 1, 2, 3, 4, 1, 4, 3, 2, 5, 6, 1, 2, 3, 8, 5, 6, 7, 4, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 1, 2, 3, 4, 7, 6, 5, 12, 11, 8, 9, 10, 1, 2, 3, 4, 7, 6, 13, 10, 9, 14, 5, 8, 11, 12, 1, 2, 3, 4, 7, 6, 5, 12, 11, 8, 9, 14, 15, 16, 13, 10, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 13, 16, 15, 14, 17, 12, 11, 18, 1, 2, 3

Offset

1,2

Comments

In the prime circle problem we seek to arrange the numbers 1 to 2n around a circle so that the sum of each pair of adjacent numbers is prime. To display the solution, we unroll the circle starting at 1.

References

R. K. Guy, Unsolved Problems Number Theory, Section C1.

Links

T. D. Noe, Rows n=1..50 of triangle, flattened

Eric Weisstein's World of Mathematics, Prime Circle

Example

Triangle begins:
1, 2;
1, 2, 3, 4;
1, 4, 3, 2, 5, 6;
1, 2, 3, 8, 5, 6, 7, 4;
...

Crossrefs

Cf. A051252 (number of solutions for each n), A051237 (prime pyramid).

Sequence in context: A353293 A162190 A349325 * A344006 A353319 A205123

Adjacent sequences: A134289 A134290 A134291 * A134293 A134294 A134295

Keyword

nice,nonn,look,tabf

Author

T. D. Noe, Oct 16 2007

Status

approved