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

0,1

Comments

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

Links

Table of n, a(n) for n=0..44.

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

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

Sequence in context: A355062 A355060 A115651 * A010417 A155568 A353485

Adjacent sequences: A062556 A062557 A062558 * A062560 A062561 A062562

Keyword

nonn

Author

Labos Elemer, Jul 03 2001

Extensions

More terms from Sean A. Irvine, Apr 03 2023

Status

approved