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.

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

Author

Labos Elemer, Jul 03 2001

Keywords

• nonn

Comments

32 is the first prime power > 1 not in this sequence.

Crossrefs

Cf. A000961, A025475, A010672, A011185, A025582, A005282.

Programs

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

Extensions

More terms from Sean A. Irvine, Apr 03 2023