OFFSET
1,1
COMMENTS
The sequence is a subset of A038550, numbers that can be expressed as the sum of k>1 consecutive positive integers in only one way. If the successive terms of the present sequence are expressed as the sum of k>1 consecutive integers and added, the result will be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11... (conjectured to extend ad infinitum).
Any sequence with this property has distinct positive terms. This is the lexicographically earliest sequence with this property.
The sequence behaves in a strange way: most of its terms are the sum of 2 or 3 consecutive integers, but sometimes huge "gaps" appear. The term a(65) = 34404982325248 is equal to 92911 + 92912 + 92913 + ... + 8295695 + 8295696 + 8295697; but a(66) = 16591397 is the sum of the next 2 consecutive terms only, 8295698 and 8295699. The term a(71) = 7893201574690816 is the sum of more than 10^8 consecutive integers(!): 8299930 + 8299931 + 8299932 + ... + 125917798.
Further indices of records are 77, 81, 89, 91, 101, 102, 106, 145, 149, 153, 157, 169, 173, 181, 191, 201, ... with a(201) ~ 10^562. - M. F. Hasler, Aug 29 2020
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..200
EXAMPLE
The 1st term is 3 = 1 + 2.
The 2nd term is 7 = 3 + 4.
The 3rd term is 11 = 5 + 6.
The 4th term is 24 = 7 + 8 + 9.
The 5th term is 46 = 10 + 11 + 12 + 13.
The 6th term is 29 = 14 + 15, etc.
PROG
(PARI) (A336897_vec(N, s=0)=vector(N, n, my(o=s++); while(!is_A038550(o+=s++), ); o)) (60) \\ slow for N >= 65. - M. F. Hasler, Aug 29 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Aug 07 2020
STATUS
approved