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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
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
Partial sums of A287178.
Sequence in context: A226471 A175510 A144643 * A328688 A291651 A078869
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

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