

A175498


a(1)=1. a(n) = the smallest positive integer not occurring earlier such that a(n)a(n1) doesn't equal a(k)a(k1) for any k with 2 <= k <= n1.


19



1, 2, 4, 3, 6, 10, 5, 11, 7, 12, 9, 16, 8, 17, 15, 23, 13, 24, 18, 28, 14, 26, 19, 32, 20, 34, 21, 36, 25, 41, 22, 39, 30, 48, 27, 46, 29, 49, 31, 52, 37, 59, 33, 56, 40, 64, 35, 60, 38, 65, 42, 68, 43, 71, 44, 73, 45, 75, 51, 82, 47, 79, 112, 50, 84, 53, 88, 54, 90, 57, 94, 55, 93, 61, 100, 58, 98, 62, 103, 63, 105, 67
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OFFSET

1,2


COMMENTS

This sequence is a permutation of the positive integers.
a(n+1)a(n) = A175499(n).
Conjecture: the lexicographically earliest permutation of {1,2,...n} for which differences of adjacent numbers are all distinct (cf. A131529) has, for n>infinity, this sequence as its prefix.  Joerg Arndt, May 27 2012


LINKS

Joerg Arndt and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000, first 1122 terms from Joerg Arndt
Index entries for sequences that are permutations of the natural numbers


MATHEMATICA

a[1] = 1; d[1] = 0; k = 1; z = 10000; zz = 120;
A[k_] := Table[a[i], {i, 1, k}]; diff[k_] := Table[d[i], {i, 1, k}];
c[k_] := Complement[Range[z, z], diff[k]];
T[k_] := a[k] + Complement[Range[z], A[k]];
Table[{h = Min[Intersection[c[k], T[k]]], a[k + 1] = a[k] + h, d[k + 1] = h, k = k + 1}, {i, 1, zz}];
u = Table[a[k], {k, 1, zz}] (* Clark Kimberling, May 13 2015 *)


PROG

(Python)
A175498_list, l, s, b1, b2 = [1, 2], 2, 3, set(), set([1])
for n in range(3, 10**5):
....i = s
....while True:
........if not (i in b1 or il in b2):
............A175498_list.append(i)
............b1.add(i)
............b2.add(il)
............l = i
............while s in b1:
................b1.remove(s)
................s += 1
............break
........i += 1 # Chai Wah Wu, Dec 15 2014
(Haskell)
import Data.List (delete)
a175498 n = a175498_list !! (n1)
a175498_list = 1 : f 1 [2..] [] where
f x zs ds = g zs where
g (y:ys)  diff `elem` ds = g ys
 otherwise = y : f y (delete y zs) (diff:ds)
where diff = y  x
 Reinhard Zumkeller, Apr 25 2015


CROSSREFS

Cf. A081145, A175499, A257465 (inverse), A257883, A131388, A131389, A257705.
Sequence in context: A113233 A051849 A283961 * A083673 A131388 A131393
Adjacent sequences: A175495 A175496 A175497 * A175499 A175500 A175501


KEYWORD

nonn,nice


AUTHOR

Leroy Quet, May 31 2010


EXTENSIONS

More terms from Sean A. Irvine, Jan 27 2011


STATUS

approved



