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A068801
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Primes that can be formed by concatenating 2^a and 3^b.
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2
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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).
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 25 2002
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STATUS
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approved
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