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%I #20 Jul 28 2019 21:48:07
%S 1,1243,1423,2143,2341,2413,2431,3241,3421,4123,4213,4231,4321,
%T 1234567,1234657,1235467,1235647,1236457,1236547,1243567,1243657,
%U 1245367,1245637,1245673,1245763,1246357,1246537,1246573,1246753
%N Permutations of lengths 1,2,3,... arranged lexicographically that are relatively prime to 30.
%C Numbers whose digits are permutations of (1,2,3,4,...,n) for some n >= 1, for which the first 3 primes (2,3,5) do not appear in their factorization. This constitutes the smallest subset of A030299 for which it's possible to synthesize a compact formula to express the generic term: it contains every prime number already in A030299.
%C In fact it corresponds to the subset of the terms of A030299 constructed from the concatenation of k:=1+3*i (for i >= 0) elements belonging to (1,2,3,4,...,n) that are congruent in modulo 10 to (1,3,7,9).
%H Marco Ripà, <a href="http://www.rudimatematici.com/Bookshelf/divisibilitaper3.pdf"> Divisibilità per 3 degli elementi di particolari sequenze numeriche</a>
%H Marco Ripà, <a href="http://www.scribd.com/doc/47337392/On-prime-factors-in-old-and-new-sequences-of-integers">On prime factors in old and new sequences of integers</a>
%t f[n_] := Select[ FromDigits@ # & /@ Permutations@ Range@ n, Mod[#, 2] != 0 && Mod[#, 3] != 0 && Mod[#, 5] != 0 &]; Take[ Flatten@ Array[f, 7], 35]
%Y Cf. A030299, A030298.
%K nonn,easy,base,less
%O 1,2
%A _Marco Ripà_, Jan 23 2011