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A372207
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a(n) is the smallest prime number that is obtained by concatenating 2 consecutive n-digit integers.
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1
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23, 1213, 102101, 10021001, 1000810007, 100010100011, 10000241000023, 1000004210000041, 100000002100000003, 10000000081000000009, 1000000000810000000007, 100000000002100000000001, 10000000000021000000000001, 1000000000001010000000000011, 100000000000002100000000000003
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OFFSET
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1,1
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COMMENTS
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It is possible to form primes by concatenating an integer with its successor (A030458), as well as by concatenating an integer with its predecessor (A052089).
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LINKS
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EXAMPLE
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a(3) = 102101, since when concatenating 3-digit numbers, the first three numbers obtained, in increasing order, are 100101, 101100, 101102, which are composite, while the next number in the list is 102101, which is prime.
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PROG
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(Python)
from sympy import isprime
def a(n):
if n == 1: return 23
lb, ub = 10**(n-1), 10**n
for k in range(lb, ub, 2):
base = k*ub
for inc in [k-1, k+1]:
if inc >= lb and isprime(t:=base+inc):
return t
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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