A203569 Numbers whose digits are a permutation of [0,...,n] and which contain the product of any two adjacent digits as a substring.

0, 10, 102, 120, 201, 210, 1203, 1302, 2013, 2031, 2103, 2130, 3012, 3021, 3102, 3120, 12034, 12043, 20314, 20413, 21304, 21403, 30214, 30412, 31204, 31402, 34012, 34120, 40213, 40312, 41203, 41302, 43012, 43120, 120345, 120543, 203145, 203154, 204153

Offset: 1

Author

M. F. Hasler, Jan 03 2012

Keywords

• nonn
• base
• fini
• full

Comments

The subsequence A198298 corresponding to n=9 was suggested by E. Angelini (cf. link).

If we consider permutations of [1,...,n], the only solutions are { 1, 12, 21, 213, 312, 3412, 4312, 71532486 }.

There are 285 terms.

Examples

			The term 12034 is in the sequence since 1*2=2, 2*0=0, 0*3=0 and 3*4=12 are all substrings of 12034. This is the least nontrivial term in the sense that it contains two adjacent digits > 1, which is the case for all solutions > 42000.
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..285 (complete sequence)
• Eric Angelini, 10 different digits, 9 products
• E. Angelini, 10 different digits, 9 products [Cached copy, with permission]
• E. Angelini, 10 different digits, 9 products, Posting to Seqfan List, Jan 03 2012

Crossrefs

Cf. A198298, A203566, A210013-A210020.

Programs

PARI

n_digit_terms(n)={ my(a=[],p=vector(n,i,10^(n-i))~,t);for(i=(n-1)!,n!-1, is_A203565(t=numtoperm(n,i)%n*p) & a=concat(a,t));vecsort(a)}