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A068710
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Primes whose digits can be arranged in increasing cyclic order - to form a substring of 123456789012345678901234567890...
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2
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2, 3, 5, 7, 23, 43, 67, 89, 109, 809, 1423, 2143, 2341, 2543, 4231, 4253, 4523, 4567, 4657, 5647, 5867, 6547, 6857, 10243, 10289, 10789, 10987, 12043, 12809, 18097, 19087, 20143, 20341, 20431, 20981, 21089, 23041, 24103, 25463, 25643, 28019, 28109, 28901, 30241, 32401, 36457, 40123, 40213, 40231, 41023
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OFFSET
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1,1
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COMMENTS
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Observe that the digits 0 and 9 do not appear in any 4-digit or 7-digit prime in this sequence. Also note that no 10-digit prime has this form (since the sum of 10 consecutive digits is divisible by 3).
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LINKS
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EXAMPLE
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2143 is a term as its digits can be arranged as 1234.
109 is a terms since the digits can be permuted to give 901.
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MATHEMATICA
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cyclicP[n_] := Module[{d = Mod[Range[n + 9], 10], ds, u, i}, ds = Partition[d, n, 1]; u = {}; Do[u = Union[u, Select[FromDigits/@Permutations[ds[[i]]], # > 10^(n - 1) && PrimeQ[#] &]], {i, 10}]; u]; Flatten[Table[cyclicP[n], {n, 7}]]
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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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Jan 22 2011: There were omissions after the term 6857 (10243 for example), so I deleted the terms beyond this point, and the presumably erroneous Mma program that accompanied them. Thanks to Marco Ripà for pointing out that there were errors. - N. J. A. Sloane
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STATUS
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approved
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