

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



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)
(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)


CROSSREFS



KEYWORD

nonn,nice,easy


AUTHOR



EXTENSIONS

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


STATUS

approved



