The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 20 08:05 EDT 2024. Contains 372703 sequences. (Running on oeis4.)