OFFSET
1,1
COMMENTS
The authors conjecture that it is impossible to extend the sequence forever if a(1) < 61.
With a(1) = 60, for instance, we will be stuck with the integer 5:
60,6,7,8,9,10,1,11,12,13,15,16,18,20,2,23,25,28,31,3,35,39,43,4,48,54,5 STOP (no unused integer can extend the sequence).
See here the sequence starting with a(1) = 60 and the cumulative sums:
60,6, 7, 8, 9, 10, 1, 11, 12, 13, 15, 16, 18, 20, 2, 23, 25, 28, 31, 3, 35,
60,66,73,81,90,100,101,112,124,137,152,167,185,205,207,230,255,283,314,317,352,
(the two lines above continue here):
39, 43, 4, 48, 54, 5, STOP
391,434,438,486,540,545.
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..5004
EXAMPLE
Here are the first terms of the sequence:
61,6,7,8,9,10,1,11,12,13,15,16,18,20,2,23,25,...
and here are the cumulative sums:
61,67,74,82,91,101,102,113,125,138,153,169,187,207,209, 232,257,...
If we align the a(n)s and the cumulative sums, we see that those always begin with the integer above it:
61,6, 7, 8, 9, 10, 1, 11, 12, 13, 15, 16, 18, 20, 2, 23, 25,...
61,67,74,82,91,101,102,113,125,138,153,169,187,207,209,232,257,...
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jul 16 2018
STATUS
approved