A203566 Numbers that contain the product of any two adjacent digits as a substring, and have at least one pair of adjacent digits > 1.

126, 153, 1025, 1052, 1126, 1153, 1260, 1261, 1262, 1530, 1531, 1535, 2045, 2054, 2126, 2137, 2153, 2173, 2204, 2214, 2306, 2316, 2408, 2418, 2510, 2612, 2714, 2816, 2918, 3056, 3065, 3126, 3153, 3206, 3216, 3309, 3319, 3412, 3515, 3618, 4022, 4058, 4085, 4122, 4126, 4153, 4208, 4218

Offset

1,1

Comments

Inspired by the problem restricted to pandigital numbers suggested by E. Angelini (cf. link).

Any number having no two adjacent digits larger than 1 is trivially in the sequence A203565, which motivated the present sequence.

In the same way, any number obtained from some a(n) of this sequence by adding any number of digits '0' and '1' on either side is again in this sequence (126 -> 1126, 1260, 1261, ...). This suggests that "primitive" numbers of this kind be defined.

Links

Table of n, a(n) for n=1..48.

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 number 126 is in the sequence since 1*2=2 and 2*6=12 are both substrings of "126".

Prog

(PARI) has(n, m)={ my(p=10^#Str(m)); until( m>n\=10, n%p==m & return(1))}
is_A203566(n)={ my(d, f=0); n>21 & vecsort(d=eval(Vec(Str(n))))[#d-1]>1 & for( i=2, #d, d[i]<2 & i++ & next; d[i-1]>1 | next; has(n, d[i]*d[i-1]) | return; f=1); f }
for( n=22, 9999, is_A203566(n) & print1(n", "))

Crossrefs

Cf. A198298, A203569, A210013-A210020.

Sequence in context: A020342 A179482 A009944 * A320292 A104395 A267331

Adjacent sequences: A203563 A203564 A203565 * A203567 A203568 A203569

Keyword

nonn,base

Author

M. F. Hasler, Jan 03 2012

Status

approved