cp's OEIS Frontend

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

%I A203566 #18 Dec 23 2024 14:53:43
%S A203566 126,153,1025,1052,1126,1153,1260,1261,1262,1530,1531,1535,2045,2054,
%T A203566 2126,2137,2153,2173,2204,2214,2306,2316,2408,2418,2510,2612,2714,
%U A203566 2816,2918,3056,3065,3126,3153,3206,3216,3309,3319,3412,3515,3618,4022,4058,4085,4122,4126,4153,4208,4218
%N A203566 Numbers that contain the product of any two adjacent digits as a substring, and have at least one pair of adjacent digits > 1.
%C A203566 Inspired by the problem restricted to pandigital numbers suggested by E. Angelini (cf. link).
%C A203566 Any number having no two adjacent digits larger than 1 is trivially in the sequence A203565, which motivated the present sequence.
%C A203566 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.
%H A203566 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm">10 different digits, 9 products</a>
%H A203566 E. Angelini, <a href="/A198298/a198298.pdf">10 different digits, 9 products</a> [Cached copy, with permission]
%H A203566 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2012-January/016213.html">10 different digits, 9 products</a>, Posting to Seqfan List, Jan 03 2012
%e A203566 The number 126 is in the sequence since 1*2=2 and 2*6=12 are both substrings of "126".
%o A203566 (PARI) has(n,m)={ my(p=10^#Str(m)); until( m>n\=10, n%p==m & return(1))}
%o A203566 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 }
%o A203566 for( n=22,9999, is_A203566(n) & print1(n","))
%Y A203566 Cf. A198298, A203569, A210013-A210020.
%K A203566 nonn,base
%O A203566 1,1
%A A203566 _M. F. Hasler_, Jan 03 2012