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

1,2

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
(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

Crossrefs

Cf. A025582, A051912, A055598.

Partial sums of A287178.

Sequence in context: A226471 A175510 A144643 * A328688 A291651 A078869

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