A068801 Primes that can be formed by concatenating 2^a and 3^b.

11, 13, 19, 23, 29, 41, 43, 83, 89, 127, 163, 181, 227, 281, 641, 643, 827, 881, 1283, 1289, 1627, 2243, 2729, 4243, 4729, 6427, 6481, 8243, 10243, 16561, 16729, 20483, 26561, 40961, 42187, 81929, 86561, 102481, 163841, 166561, 219683, 326561, 327689, 859049

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..8482

Example

8243 is a concatenation of 2^3 and 3^5. 10242187 is a term as a concatenation of 1024 (=2^10) and 2187(=3^7).

Prog

(Python)
from sympy import isprime
from itertools import count, takewhile
def auptod(digits):
    M = 10**digits
    pows2 = list(takewhile(lambda x: x < M , (2**a for a in count(0))))
    pows3 = list(takewhile(lambda x: x < M , (3**b for b in count(0))))
    strs2, strs3 = list(map(str, pows2)), list(map(str, pows3))
    concat = (int(s2+s3) for s2 in strs2 for s3 in strs3)
    return sorted(set(t for t in concat if t < M and isprime(t)))
print(auptod(6)) # Michael S. Branicky, Aug 17 2022

Crossrefs

Cf. A068712, A068714.

Sequence in context: A330696 A103803 A188677 * A215504 A342406 A109650

Adjacent sequences: A068798 A068799 A068800 * A068802 A068803 A068804

Keyword

base,nonn

Author

Amarnath Murthy, Mar 05 2002

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 25 2002

a(43) and beyond from Michael S. Branicky, Aug 17 2022

Status

approved