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

Author

M. F. Hasler, Jan 03 2012

Keywords

• nonn
• base

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.

Examples

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

Links

• 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, A203569, A210013-A210020.

Programs

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","))