

A034757


a(1)=1, a(n) = smallest odd number such that all sums of pairs of (not necessarily distinct) terms in the sequence are distinct.


3



1, 3, 7, 15, 25, 41, 61, 89, 131, 161, 193, 245, 295, 363, 407, 503, 579, 721, 801, 949, 1129, 1185, 1323, 1549, 1643, 1831, 1939, 2031, 2317, 2623, 2789, 3045, 3143, 3641, 3791, 4057, 4507, 4757, 5019, 5559, 5849, 6309, 6707, 7181, 7593
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OFFSET

1,2


COMMENTS

a(1) = 1, a(n) = least number such that every difference a(i)a(j) is a distinct even number.  Amarnath Murthy, Apr 07 2004


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = 2*A005282(n)1. (David Wasserman)


EXAMPLE

5 is not in the sequence since 5+1 is already obtainable from 3+3, 9 is excluded since 1, 3 and 7 are in the sequence and would collide with 1+9


MATHEMATICA

seq2={1, 3}; Do[le=Length[seq2]; t=Last[seq2]+2; While[Length[Expand[(Plus @@ (x^seq2) + x^t)^2]] < Pochhammer[3, le]/le!, t=t+2]; AppendTo[seq2, t], {20}]; Print@seq2


PROG

(Haskell)
a034757 = (subtract 1) . (* 2) . a005282  Reinhard Zumkeller, Dec 18 2012


CROSSREFS

Cf. A025582, A051912, A055598.
Sequence in context: A226471 A175510 A144643 * A291651 A078869 A011890
Adjacent sequences: A034754 A034755 A034756 * A034758 A034759 A034760


KEYWORD

nonn,nice,easy


AUTHOR

Wouter Meeussen, Jun 01 2000


EXTENSIONS

An incorrect comment from Amarnath Murthy, also dated Apr 07 2004, has been deleted.
Offset fixed by Reinhard Zumkeller, Dec 18 2012


STATUS

approved



