OFFSET
1,2
COMMENTS
Charles R Greathouse IV asked for a proof showing that this sequence is infinite (SeqFan mailing list, Jan 2014).
Significant jumps occur at a(3)=4=2*a(2), a(5)=10=2*a(4), a(9)=28=2*a(8), a(17)=82=2*a(16), a(31)=236 >> a(29)=122, a(47)=628 >> a(44)=302, a(70)=1622 >> a(66)=809, a(90)=4165 >> a(87)=2062, ... . Here, the size of the terms roughly doubles over the interval of very few indices. The indices such that a(n[k]) >= 2*a(n[k-1]) are n[k] = 3, 5, 9, 17, 30, 46, 69, 89, ... .
This sequence first differs from A003278 at the 21st term, which is 92 here but 91 in A003278. Up to 91, each natural number n that did not appear in this sequence failed to do so because there were two smaller numbers n-a and n-2a, with A229037(n-a) and A229037(n-2a) both equal to 1. 91 is missing from this sequence; in other words, A229037(91) is not 1, because A229037(27) = 9 and A229037(59) = 5. - Jack W Grahl, Dec 28 2014
LINKS
Charles R Greathouse IV and Chai Wah Wu, Table of n, a(n) for n = 1..434, First 266 terms from Charles R Greathouse IV.
Charles R Greathouse IV, [seqfan] Lexicographically first 3-free sequence (2014)
PROG
(Haskell)
a236246 n = a236246_list !! (n-1)
a236246_list = filter ((== 1) . a229037) [1..]
-- Reinhard Zumkeller, Apr 26 2014
(Python)
for n in range(10**6):
....i, j, b = 1, 1, set()
....while n-2*i >= 0:
........i += 1
........while j in b:
............b.remove(j)
............j += 1
....A229037_list.append(j)
....if j == 1:
........A236246_list.append(n+1) # Chai Wah Wu, Dec 25 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 20 2014
STATUS
approved