A107346 Differences between successive permutations of 1,2,3,4,5 regarded as decimal numbers arranged in increasing order.

9, 81, 18, 81, 9, 702, 9, 171, 27, 72, 18, 693, 18, 72, 27, 171, 9, 702, 9, 81, 18, 81, 9, 5913, 9, 81, 18, 81, 9, 1602, 9, 261, 36, 63, 27, 594, 18, 162, 36, 162, 18, 603, 9, 171, 27, 72, 18, 5814, 9, 171, 27, 72, 18, 603, 9, 261, 36, 63, 27, 1584, 27, 63, 36, 261, 9

Offset: 1

Author

Ivan Meyer (ivan.mey(AT)gmail.com), May 23 2005

Keywords

• easy
• nonn
• base
• fini
• full

Comments

We can produce similar sequences of length n!-1 from all the n-set permutations (1,...,n), starting from n=2 up to n=9. The next larger sequence contains always the preceding sequence as its proper prefix. See A219664 for the largest such sequence. - Antti Karttunen, Dec 18 2012

See A209280 for the extension of this sequence to 9!-1 terms, and for comments and formulas which apply to this subsequence. - M. F. Hasler, Jan 15 2013

Examples

			Permutations are 12345, 12354, 12435, ...
a(3) = 18 because if we order these permutations (ascending), then P(4)-P(3) = 12453-12435 = 18
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..119 (complete sequence)

Crossrefs

Cf. A030299, A219664, A209280.

Programs

Mathematica

Differences[FromDigits /@ Permutations[{1, 2, 3, 4, 5}]] (* T. D. Noe, Dec 18 2012 *)

PARI

A107346(n)=A209280(n) \\ - M. F. Hasler, Jan 15 2013

Formula

a(n) = A209280(n) for n<5!. See there for more useful relations. - M. F. Hasler, Jan 15 2013