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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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T. D. Noe and David Consiglio, Jr., Table of n, a(n) for n = 1..9463 (terms < 5 x 10^7. The 1287 terms < 10^7 were entered by T. D. Noe.)
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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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Cf. A068708, A068709. See A177119 for a different (and finite) version.
Sequence in context: A106711 A048398 A059170 * A120805 A177119 A096265
Adjacent sequences: A068707 A068708 A068709 * A068711 A068712 A068713
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KEYWORD
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base,nonn,more
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AUTHOR
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Amarnath Murthy and V.P.Singh (amarnath_murthy(AT)yahoo.com), Mar 05 2002
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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
Corrected by T. D. Noe, Jan 24 2011
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STATUS
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approved
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