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.

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

Offset: 1

Author

Wouter Meeussen, Jun 01 2000

Keywords

• nonn
• nice
• easy

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

Examples

			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
		

Links

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

Crossrefs

Cf. A025582, A051912, A055598.

Partial sums of A287178.

Programs

Haskell

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

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

Python

from itertools import count, islice
def A034757_gen(): # generator of terms
    aset1, aset2, alist = set(), set(), []
    for k in count(1,2):
        bset2 = {k<<1}
        if (k<<1) not in aset2:
            for d in aset1:
                if (m:=d+k) in aset2:
                    break
                bset2.add(m)
            else:
                yield k
                alist.append(k)
                aset1.add(k)
                aset2.update(bset2)
A034757_list = list(islice(A034757_gen(),30)) # Chai Wah Wu, Sep 05 2023

Formula

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

Extensions

An incorrect comment from Amarnath Murthy, also dated Apr 07 2004, has been deleted.

Offset fixed by Reinhard Zumkeller, Dec 18 2012