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A062559
A B2 sequence consisting of powers of primes but not primes: a(n) = least value from A025475 such that sequence increases and pairwise sums of distinct elements are all distinct.
0
4, 8, 9, 16, 25, 27, 49, 64, 121, 243, 256, 343, 512, 729, 961, 1024, 1331, 1369, 1849, 2048, 2187, 2197, 2401, 3125, 3481, 4096, 4913, 5329, 6561, 6859, 6889, 8192, 10201, 12769, 14641, 15625, 16384, 16807, 19683, 22201, 22801, 27889, 28561, 29791, 32768
OFFSET
0,1
COMMENTS
32 is the first prime power > 1 not in this sequence.
PROG
(Python)
from itertools import count, islice
from sympy import factorint
def A062559_gen(): # generator of terms
aset2, alist = set(), []
for k in count(0):
if len(f:=factorint(k).values()) == 1 and max(f) > 1:
bset2 = set()
for a in alist:
if (b:=a+k) in aset2:
break
bset2.add(b)
else:
yield k
alist.append(k)
aset2.update(bset2)
A062559_list = list(islice(A062559_gen(), 30)) # Chai Wah Wu, Sep 11 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 03 2001
EXTENSIONS
More terms from Sean A. Irvine, Apr 03 2023
STATUS
approved