A181073 Permutations of lengths 1,2,3,... arranged lexicographically that are relatively prime to 30.

1, 1243, 1423, 2143, 2341, 2413, 2431, 3241, 3421, 4123, 4213, 4231, 4321, 1234567, 1234657, 1235467, 1235647, 1236457, 1236547, 1243567, 1243657, 1245367, 1245637, 1245673, 1245763, 1246357, 1246537, 1246573, 1246753

Offset

1,2

Comments

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.

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).

Links

Table of n, a(n) for n=1..29.

Marco Ripà, Divisibilità per 3 degli elementi di particolari sequenze numeriche

Marco Ripà, On prime factors in old and new sequences of integers

Mathematica

f[n_] := Select[ FromDigits@ # & /@ Permutations@ Range@ n, Mod[#, 2] != 0 && Mod[#, 3] != 0 && Mod[#, 5] != 0 &]; Take[ Flatten@ Array[f, 7], 35]

Crossrefs

Cf. A030299, A030298.

Sequence in context: A209711 A228964 A047628 * A023065 A190413 A252675

Adjacent sequences: A181070 A181071 A181072 * A181074 A181075 A181076

Keyword

nonn,easy,base,less

Author

Marco Ripà, Jan 23 2011

Status

approved