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

1,2

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.

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

Example

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.

Prog

(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)}

Crossrefs

Cf. A198298, A203566, A210013-A210020.

Sequence in context: A039393 A199168 A297062 * A305712 A053041 A220491

Adjacent sequences: A203566 A203567 A203568 * A203570 A203571 A203572

Keyword

nonn,base,fini,full

Author

M. F. Hasler, Jan 03 2012

Status

approved