A068801 - OEIS

%I #7 Aug 17 2022 16:11:59

%S 11,13,19,23,29,41,43,83,89,127,163,181,227,281,641,643,827,881,1283,

%T 1289,1627,2243,2729,4243,4729,6427,6481,8243,10243,16561,16729,20483,

%U 26561,40961,42187,81929,86561,102481,163841,166561,219683,326561,327689,859049

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

%H Michael S. Branicky, <a href="/A068801/b068801.txt">Table of n, a(n) for n = 1..8482</a>

%e 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).

%o (Python)

%o from sympy import isprime

%o from itertools import count, takewhile

%o def auptod(digits):

%o     M = 10**digits

%o     pows2 = list(takewhile(lambda x: x < M , (2**a for a in count(0))))

%o     pows3 = list(takewhile(lambda x: x < M , (3**b for b in count(0))))

%o     strs2, strs3 = list(map(str, pows2)), list(map(str, pows3))

%o     concat = (int(s2+s3) for s2 in strs2 for s3 in strs3)

%o     return sorted(set(t for t in concat if t < M and isprime(t)))

%o print(auptod(6)) # _Michael S. Branicky_, Aug 17 2022

%Y Cf. A068712, A068714.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Mar 05 2002

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

%E a(43) and beyond from _Michael S. Branicky_, Aug 17 2022