A329894 Terms of A025487 from which the distance to the next larger prime is a composite number.

512, 16384, 373248, 393216, 524288, 1119744, 4194304, 4718592, 5971968, 8388608, 10077696, 10616832, 17915904, 21233664, 31104000, 33554432, 35831808, 42467328, 47775744, 56623104, 67108864, 150994944, 159252480, 286654464, 322486272, 362797056, 679477248, 859963392, 1528823808, 2176782336, 2890137600, 4294967296, 5804752896, 8748000000

Offset

1,1

Comments

From the first 795641 terms of A025487 (terms that are in range 1 .. 2^101) only 4238 (~ 0.5 %) are included in this sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..4238

Example

As A151800(512) = 521, with 521 - 512 = 9 (a composite number), 512 is included in this sequence.

Prog

(PARI)
isc(n) = ((n > 1)&&!isprime(n));
for(n=1, 2000, if(isc(nextprime(1+A025487(n))-A025487(n)), print1(A025487(n), ", ")));
(Python)
from itertools import islice
from heapq import heappop, heappush
from sympy import nextprime, isprime, factorint, prevprime
def A329894_gen(): # generator of terms
    h, hset = [1], {1}
    while True:
        m = heappop(h)
        q = nextprime(m)
        if q-m>1 and not isprime(q-m):
            yield m
        ps = factorint(m)
        for p in ps:
            if p == 2 or ps[prevprime(p)]>ps[p]:
                mp = m*p
                if mp not in hset:
                    heappush(h, mp)
                    hset.add(mp)
        mp = m*nextprime(max(ps.keys(), default=1))
        if mp not in hset:
            heappush(h, mp)
            hset.add(mp)
A329894_list = list(islice(A329894_gen(), 30)) # Chai Wah Wu, Mar 24 2026

Crossrefs

Cf. A025487, A129912, A141345, A151800.

Sequence in context: A254252 A200791 A254812 * A258523 A257147 A254579

Adjacent sequences: A329891 A329892 A329893 * A329895 A329896 A329897

Keyword

nonn

Author

Antti Karttunen, Dec 24 2019

Status

approved