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A203566
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Numbers that contain the product of any two adjacent digits as a substring, and have at least one pair of adjacent digits > 1.
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13
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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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
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EXAMPLE
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The number 126 is in the sequence since 1*2=2 and 2*6=12 are both substrings of "126".
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PROG
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(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", "))
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CROSSREFS
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Cf. A198298, A203569, A210013-A210020.
Sequence in context: A020342 A179482 A009944 * A320292 A104395 A267331
Adjacent sequences: A203563 A203564 A203565 * A203567 A203568 A203569
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KEYWORD
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nonn,base
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AUTHOR
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M. F. Hasler, Jan 03 2012
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STATUS
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approved
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