A395332 Smallest n-digit base-3 deletable prime.

2, 5, 11, 29, 83, 251, 809, 2267, 6803, 20231, 59699, 177797, 533063, 1599203, 4798091, 14394131, 43104077, 129509579, 387893609, 1163369621, 3488010587, 10461810473, 31385429963, 94154205701, 282459695381, 847320895613, 2541962686727, 7625868891857, 22877166983813

Offset

1,1

Comments

A base-3 deletable prime is a prime whose base-3 representation can be reduced to the single-digit prime 2 by deleting one digit at a time, without ever creating a leading zero, so that every intermediate value is prime. a(n) is the smallest such prime with exactly n digits in base 3. This is the base-3 analog of A125589 (base 10).

Links

Daniel Okwor, Table of n, a(n) for n = 1..35

Daniel Okwor, A Computational Study of Base-b Deletable Primes, Zenodo, 2026; also at Orygn Research.

Example

a(2) = 5: in base 3, 5 is written 12; deleting the digit 1 leaves 2, which is prime.
a(5) = 83: in base 3, 83 is written 10002; the deletions 10002 -> 1002 -> 102 -> 12 -> 2 (base 3) correspond to the primes 83, 29, 11, 5, 2.

Prog

(Python)
from sympy import isprime
def to3(n):
    s=""
    while n: s=str(n%3)+s; n//=3
    return s
def deletable(p):
    s=to3(p)
    if len(s)==1: return isprime(p)
    for i in range(len(s)):
        t=s[:i]+s[i+1:]
        if t[0]=="0": continue
        v=int(t, 3)
        if isprime(v) and deletable(v): return True
    return False
def a(n):
    for p in range(3**(n-1), 3**n):
        if isprime(p) and deletable(p): return p
print([a(n) for n in range(1, 12)])

Crossrefs

Cf. A096236, A125589, A125590, A305352, A395333.

Sequence in context: A360810 A320171 A014211 * A389715 A160911 A092764

Adjacent sequences: A395328 A395330 A395331 * A395333 A395334 A395335

Keyword

nonn,base,new

Author

Daniel Okwor, Jun 15 2026

Status

approved