cp's OEIS Frontend

A182273 Starting with 1, smallest integer not having a zero and not yet in the sequence such that two neighboring digits of the sequence multiply to a composite.

%I A182273 #27 Feb 03 2025 13:54:22
%S A182273 1,4,2,3,5,6,7,8,9,14,16,18,19,22,23,24,25,26,27,28,29,32,33,34,35,36,
%T A182273 37,38,39,41,42,43,44,45,46,47,48,49,52,53,54,55,56,57,58,59,61,62,63,
%U A182273 64,65,66,67,68,69,72,73,74,75,76,77,78,79,81,82,83,84
%N A182273 Starting with 1, smallest integer not having a zero and not yet in the sequence such that two neighboring digits of the sequence multiply to a composite.
%C A182273 The number after 1 has to be 4, because the product 1*4 must be composite.
%C A182273 Then 2 is OK, because 4*2 = 8 is composite.
%C A182273 Then 3, because 2*3 = 6 is composite, and so on.
%C A182273 Note that 14 is the term after 9 because 10 is now the smallest candidate, but 10 has a 0 digit, 11 consists of two unit digits, and 12 and 13 have digit products 2 and 3, which are prime. - _T. D. Noe_, Apr 25 2012
%H A182273 Dominic McCarty, <a href="/A182273/b182273.txt">Table of n, a(n) for n = 1..10000</a>
%o A182273 (Python)
%o A182273 a, z = [1], [1,2,3,5,7]
%o A182273 while len(a) < 100:
%o A182273     k, s = 2, "2"
%o A182273     while (k in a) or ("0" in s) or (a[-1] % 10 * int(s[0]) in z) or \
%o A182273         any(int(s[n]) * int(s[n+1]) in z for n in range(0, len(s)-1)): s, k = str(k+1), k+1
%o A182273     a.append(k)
%o A182273 print(a) # _Dominic McCarty_, Jan 30 2025
%Y A182273 Cf. A182272.
%K A182273 nonn,base,easy,nice
%O A182273 1,2
%A A182273 _Jim Nastos_ and _Eric Angelini_, Apr 22 2012