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A057630
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Primes such that replacing each digit d with d copies of the digit d produces a prime. Zeros are allowed.
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3
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11, 31, 53, 101, 131, 149, 223, 283, 311, 313, 331, 397, 463, 503, 641, 691, 937, 941, 1031, 1049, 1069, 1301, 1409, 1439, 1511, 1609, 1741, 1871, 1949, 1993, 1999, 2083, 2111, 2203, 2447, 2803, 2939, 3001, 3011, 3061, 3163, 3301, 3391, 3433, 3499, 3559
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OFFSET
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1,1
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COMMENTS
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"Replacing each digit d with d copies of the digit d" is the function A048376, well defined on the set of positive integers. Therefore (the range of) the present sequence is the largest subset of A000040 stable under the operation A048376.
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LINKS
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EXAMPLE
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E.g. 641 becomes 66666644441 which is also prime.
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MATHEMATICA
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Select[Prime[Range[500]], PrimeQ[FromDigits[Flatten[Table[#, {#}]&/@ IntegerDigits[ #]]]]&] (* Harvey P. Dale, Dec 18 2010 *)
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PROG
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(Python)
from sympy import isprime, nextprime
A057630_list, dlist, p = [], [str(d)*d for d in range(10)], 2
if isprime(int(''.join(dlist[int(d)] for d in str(p)))):
p = nextprime(p) # Chai Wah Wu, Dec 19 2019, corrected Jan 01 2022
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CROSSREFS
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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EXTENSIONS
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Offset changed to 1, according to OEIS conventions, by M. F. Hasler, Jan 23 2013
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STATUS
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approved
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