A068710 Primes whose digits can be arranged in increasing cyclic order - to form a substring of 123456789012345678901234567890...

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

Offset: 1

Author

Amarnath Murthy and V. P. Singh, Mar 05 2002

Keywords

• base
• nonn

Comments

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).

Examples

			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.
		

Links

• 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.)

Crossrefs

Cf. A068708, A068709. See A177119 for a different (and finite) version.

Programs

Mathematica

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}]]

Extensions

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