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A227775
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Smallest prime that is a concatenation in base n of two or more successive numbers beginning with a power of n (including n^0=1).
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1
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OFFSET
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2,1
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COMMENTS
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Terms computed by expanding the print for the program at A173189 (to include the variable r).
a(10) consists of 10^13 followed by 10^13+k, k=1 to 9 in order (140 digits), and then follow 13 and 1741. a(13) has 258 decimal digits, and then 227, 17, 320255973501901, 19 and 5851 follow before a P209 arises for n=19 (n=31 produces the next prime that would not fit a mainline sequence here, at 467 digits; and the number for n=67, the concatenation in that base of 67^19 through 67^19+525, is a whopping 19209 decimal digits). Terms through at least n=78 may be found in a reasonable time using the program (and sped up by a small factor if it is modified to only search for r). a(79) is very large, however, and has a high heuristic probability of being beyond current computational means, as candidates having the right number of numbers concatenated to avoid being divisible by a small prime arise only about once every 11 orders of magnitude.
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LINKS
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FORMULA
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a(p-2) = p if p is an odd prime.
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EXAMPLE
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11 is the decimal representation of the value for n=2 as the concatenation 10 followed by 11 in binary, with the only smaller concatenation of type (110, 6 in decimal) composite.
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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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STATUS
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approved
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