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

1,1

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

Links

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

Example

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

Maple

See A225376.

Crossrefs

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

Sequence in context: A155569 A189484 A155567 * A036667 A371843 A056016

Adjacent sequences: A225374 A225375 A225376 * A225378 A225379 A225380

Keyword

nonn

Author

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

Extensions

Corrected and edited by Christopher Carl Heckman, May 12 2013

Status

approved