A131937 a(1)=1; a(2)=4, a(n) = a(n-1) + (n-th positive integer which does not occur in sequence A131938).

1, 4, 8, 14, 21, 29, 38, 49, 61, 74, 88, 103, 120, 138, 157, 177, 198, 220, 244, 269, 295, 322, 350, 379, 409, 440, 473, 507, 542, 578, 615, 653, 692, 732, 773, 816, 860, 905, 951, 998, 1046, 1095, 1145, 1196, 1248, 1302, 1357, 1413, 1470, 1528, 1587, 1647

Offset

1,2

Comments

Conjecture: Starting with any infinite positive integer sequence A1(n) whose complement is also infinite, let B1(n) be the sequence of partial sums of the complement of sequence A1. Let A2(n) be the sequence of partial sums of the complement of sequence B1. Iteratively let B[k](n) be the sequence of partial sums of the complement of sequence A[k], and let A[k+1](n) be the sequence of partial sums of the complement of sequence B[k]. Call the stable iterative limit sequences A(n) and B(n), which are universal and do not depend upon the initial sequence A1(n). These two limiting sequences are conjectured to be A131938 and this A131937. - Gregory Gerard Wojnar, Dec 12 2024

Links

Table of n, a(n) for n=1..52.

Example

A131938: 2,5,10,16,23,32,42,53,...
Positive integers not in A131938: 1,3,4,6,7,8,9,11,...
So a(8) = a(7) + 11 = 49.

Crossrefs

Cf. A131938.

Sequence in context: A312697 A312698 A312699 * A183857 A088804 A374505

Adjacent sequences: A131934 A131935 A131936 * A131938 A131939 A131940

Keyword

nonn,changed

Author

Leroy Quet, Jul 30 2007

Extensions

More terms from Farideh Firoozbakht, Aug 07 2007

a(51)-a(52) from Ray Chandler, Mar 06 2010

Status

approved