

A236246


Indices n for which A229037(n)=1.


3



1, 2, 4, 5, 10, 11, 13, 14, 28, 29, 31, 32, 37, 38, 40, 41, 82, 83, 85, 86, 92, 93, 96, 105, 111, 112, 115, 116, 122, 177, 236, 237, 244, 245, 247, 266, 267, 270, 276, 277, 283, 294, 301, 302, 347, 558, 628, 638, 646, 647, 649, 655, 669, 674, 685, 686
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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[k1]) 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 na and n2a, with A229037(na) and A229037(n2a) 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 3free sequence (2014)


PROG

(Haskell)
a236246 n = a236246_list !! (n1)
a236246_list = filter ((== 1) . a229037) [1..]
 Reinhard Zumkeller, Apr 26 2014
(Python)
A236246_list, A229037_list = [], []
for n in range(10**6):
....i, j, b = 1, 1, set()
....while n2*i >= 0:
........b.add(2*A229037_list[ni]A229037_list[n2*i])
........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

Subsequence of A241673.
Sequence in context: A275482 A156799 A003278 * A004792 A167795 A138048
Adjacent sequences: A236243 A236244 A236245 * A236247 A236248 A236249


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jan 20 2014


STATUS

approved



