A225377 Construct sequences P,Q,R by the rules: Q = first differences of P, R = second differences of P, P starts with 1,5,11, Q starts with 4,6, R starts with 2; at each stage the smallest number not yet present in P,Q,R is appended to R; every number appears exactly once in the union of P,Q,R. Sequence gives Q.

4, 6, 9, 16, 24, 34, 46, 59, 73, 88, 105, 123, 142, 163, 185, 208, 233, 259, 286, 314, 343, 373, 404, 436, 469, 504, 541, 579, 618, 658, 699, 741, 784, 828, 873, 920, 968, 1017, 1067, 1118, 1170

Offset: 1

Author

N. J. A. Sloane, May 12 2013, based on email from Christopher Carl Heckman, May 06 2013

Keywords

• nonn

Comments

P can be extended for 10^6 terms, but it is not known if P,Q,R can be extended to infinity.

A probabilistic argument suggests that P, Q, R are infinite. - N. J. A. Sloane, May 19 2013

Examples

			The initial terms of P, Q, R are:
1     5    11    20    36    60    94   140   199   272   360
   4     6     9    16    24    34    46    59    73    88
      2     3     7     8    10    12    13    14    15
		

Links

• Christopher Carl Heckman, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A225376, A225378, A005228, A030124, A037257.

Programs

Maple

See A225376.

Extensions

Corrected and edited by Christopher Carl Heckman, May 12 2013